Maximal Factorization of Operators Acting in Kothe-Bochner Spaces

[EN] Using some representation results for Kothe-Bochner spaces of vector valued functions by means of vector measures, we analyze the maximal extension for some classes of linear operators acting in these spaces. A factorization result is provided, and a specific representation of the biggest vector valued function space to which the operator can be extended is given. Thus, we present a generalization of the optimal domain theorem for some types of operators on Banach function spaces involving domination inequalities and compactness. In particular, we show that an operator acting in Bochner spaces of p-integrable functions for any 1First author is supported by Grant MTM2011-23164 of the Ministerio de Economia y Competitividad (Spain). Second author is supported by Grant 284110 of CONACyT (Mexico). Fourth author is supported by Grant MTM2016-77054-C2-1-P of the Ministerio de Ciencia, Innovacion y Universidades, Agencia Estatal de Investigaciones (Spain) and FEDER.Calabuig, JM.; Fernández-Unzueta, M.; Galaz-Fontes, F.; Sánchez Pérez, EA. (2021). Maximal Factorization of Operators Acting in Kothe-Bochner Spaces. Journal of Geometric Analysis. 31(1):560-578. https://doi.org/10.1007/s12220-019-00290-4S56057831

Equivalent norms in a banach function space and the subsequence property

[EN] Consider a finite measure space (Omega, Sigma, mu) and a Banach space X(mu) consisting of (equivalence classes of) real measurable functions defined on Omega such that f chi(A) is an element of X(mu) and parallel to f chi(A)parallel to <= parallel to f parallel to, for all f is an element of X(mu), A is an element of Sigma. We prove that if it satisfies the subsequence property, then it is an ideal of measurable functions and has an equivalent norm under which it is a Banach function space. As an application we characterize norms that are equivalent to a Banach function space norm.All the authors were supported by Ministerio de Ciencia, Innovacion y Universidades (Spain), Agencia Estatal de Investigaciones, and FEDER. J.M. Calabuig and M. Fernandez-Unzueta under project MTM2014-53009-P. F. Galaz-Fontes under project MTM2009-14483-C02-01 and E. A. Sanchez Perez under project MTM2016-77054-C2-1-P. M. FernandezUnzueta was also supported by CONACYT 284110.Calabuig, JM.; Fernández-Unzueta, M.; Galaz-Fontes, F.; Sánchez Pérez, EA. (2019). Equivalent norms in a banach function space and the subsequence property. Journal of the Korean Mathematical Society. 56(5):1387-1401. https://doi.org/10.4134/JKMS.j180682S1387140156

Ultraviolet spectroscopy of the hotspot in the classical T Tauri star DI Cep: Observational indications of magnetically channelled accretion

T Tauri stars (TTS) are low-mass pre-main-sequence stars that are accreting mass from the surrounding disc. The hotspots detected in some of them are probably heated by the release of gravitational energy in the accretion of the disc material on to the star. In this work we study the UV spectrum of the hotspot detected in DI Cep to constrain the physical mechanisms heating the spot and to study the possible role of the magnetic field in channelling the accretion flow. DI Cep is a classical TTS, classified as G8 IV, with a hotspot (T similar to 8500 K) covering 1-3 per cent of the visible hemisphere. We have carried out a monitoring campaign with the Short Wavelength spectrograph (1200-2000 Angstrom) and the optical FES Camera of the International Ultraviolet Explorer (IUE) from 1992 July 12 to 26. The UV spectrum of DI Cep shows excess emission in the continuum from 1700 Angstrom towards longer wavelengths with respect to a G8 IV star. The far-UV spectrum is dominated by strong emission lines of OI, CIV, Si IV, Si II and Si III], with typical surface fluxes of similar to 10(6) erg cm(-2) s(-1). The UV fluxes (lines and continuum) vary in phase and reach the maximum when the optical flux (FES) does. The light curves are similar in all the lines: the emission from the hotspot is detected above a baseline flwe probably produced by the stellar atmosphere. There is a broad range of temperatures in the hotspot (from 10(4) to 10.5 K) that is similar to that observed in the plages of magnetically active cool stars (e.g. II Peg). However, in DI Cep the light cuwes of the UV lines and continuum are correlated with the optical continuum (T/-bnnd) light curve. DI Cep as a whole deviates only slightly from active stars in the CIV-Si II and CIV-CII flux-flux relations (there is a factor of 2 excess of Si II with respect to CIV when compared with the regression line fitted to active stars). This suggests that the chromosphere and transition region of DI Cep are heated by a mechanism similar to that of the active main-sequence stars. However, the spot is significantly shifted from these relations in the flux-flux diagrams, displaying an excess of Si II (or a defect of CIV) with respect to the surface fluxes emitted by magnetically active stars. The spot alone radiates as much energy as the rest of the atmosphere, and the spot surface fluxes are similar to 10(8) erg cm(-2) s(-1) (typically 2 orders of magnitude larger than those corresponding to the atmosphere). Our observations support the theories in which the accreting material is magnetically channelled on to the stellar surface. Variations in the temperature of the spot between observations taken 1 year apart suggest that the infalling material is more likely channelled by a transient loop structure attached to the star than by a strong stellar dipolar field. The total energy radiated in the far UV lines plus the UV continuum excess is greater than or equal to 0.07 L.. This can be accounted for by the accretion of greater than or equal to 6x10(-9) M. yr(-1) from the corotation radius (8.3 R*)

Prescripción inducida en atención primaria de la Comarca Bilbao

ObjetivosPrincipales: conocer la proporción de prescripción inducida (PI) en Comarca Bilbao y su procedencia, la proporción de gasto correspondiente a la PI, la proporción de PI en los principales grupos terapéuticos, la actitud del médico de atención primaria ante la prescripción solicitada y su influencia en el gasto, la proporción de desacuerdo con dicha prescripción y los motivos de desacuerdo, y la proporción con informe del especialista. Secundarios: conocer la proporción de PI en los demás grupos terapéuticos, en fármacos VINE, EFG y en los de nula o baja mejora terapéutica.Diseño.Estudio transversal, descriptivoEmplazamientoAtención primariaParticipantesFármacos financiables prescritos por y/o solicitados a los médicos de familia de EAP.Resultados principalesSe estudiaron 7.922 fármacos. Tipo de prescripción: PI, 48,3% (IC del 95%, 47,2–49,4); del médico de atención primaria (PRO), 50,6% (IC del 95%, 49,5–51,7); desconocida, 1,1% (IC del 95%, 0,9–1,3). Procedencia principal: especialista público (72,2%), especialista privado (16,6%). Un 62,5% del gasto correspondió a la PI. En el grupo terapéutico más prescrito, sistema nervioso central (24,2%), PI, 39,8%; PRO, 58,9%; en aparato cardiovascular (19,1%), PI, 56,2%, PRO, 43,1%. Se prescribió el fármaco solicitado en un 98,4% de los casos, se cambio en el 1,2% y se suprimió en un 0,4%. Proporción de desacuerdo, 11%; motivos de desacuerdo, no hay necesidad de tratar (23,9%), grupo terapéutico (34,4%), principio activo (13,2%), marca comercial (28,5%). Hubo informe de especialista en un 62,4% de los casos.ConclusionesSe detecta una proporción considerable de prescripción no atribuible a atención primaria y una proporción importante de fármacos que el médico de primaria prescribe sin estar de acuerdo. Sería necesario un sistema que permitiera separar el gasto por niveles, así como mejorar la comunicación entre éstos.ObjectivesMain objetives: to know the proportion of induced prescription (IP) in Area Bilbao and its source, the proportion of cost IP accounts for, the proportion of IP in the main therapeutic groups, the attitude of GP when requested for prescription and its influence on cost, the proportion of disagreement with requested prescription, the reasons for disagreement, and the proportion with letter from specialist. Secondary objectives: to know the proportion of IP in the remaining therapeutic groups, in drugs of low clinical value, in generic drugs and in new drugs with low or no therapeutic improvement.DesignA descriptive cross-sectional study.SettingPrimary health care.ParticipantsDrugs prescribable under National Health Service prescribed by and/or requested to GPs.Main results7.922 drugs were analysed. Type of prescription: IP, 48.3% (95% CI, 47.2–49.4); GP prescription (GPP), 50.6% (95% CI, 49.5–51.7); unknown source, 1,1% (95% CI, 0.9–1.3). Main source, public specialist (72.2%), private specialist (16.6%). IP accounted for 62.5% of cost. In the most prescribed therapeutic group, central nervous system (24.2%), IP, 39.8%; GPP, 58.9%; in cardiovascular system (19.1%), IP, 56.2%; GPP, 43.1%. 98.4% of requested prescription was actually prescribed, 1.2% was changed and 0.4%, suppressed. Proportion of disagreement, 11%; reasons for disagreement, no need for medical treatment (23.9%), therapeutic group (34.4%), active ingredient (13.2%), brand name (28.5%). There was a 62.4% with letter from specialist.ConclusionsPrimary care is not accountable for a substantial proportion of prescription. GP prescribes a considerable proportion of drugs without agreement. It would be necessary a system that allows to separate the cost by care levels and also improve their communication

Pathway Analysis to Determine Factors Contributing to Overall Quality Scores in Four Berry Crops

Fruit quality attributes are influenced by environmental, agronomic and genetic factors; both cultivars and growing conditions can vary substantially between UK production and imported fruit. This study aimed to record and dissect the most relevant fruit quality traits for berries imported into the UK in the winter months. Blackberry, blueberry, raspberry and strawberry fruit were imported from 11 countries into a Kent-based packhouse (UK) or purchased from major retailers between December 2018 and March 2019. Multiple fruit quality components were assessed for relative contribution towards a high “overall assessment” fruit quality score. It was found that strawberry and blackberry overall scores were affected by sweetness perception, whereas blueberry and raspberry organoleptics are more complex, with overall scores influenced by flavor perception. Multiple raspberry and strawberry fruit quality traits were found to be associated with genotypic differences, indicating a promising potential for genetic improvement through breeding. By contrast, the study findings suggest that there is less potential for genetic improvement in blueberry, and that the environment may have a large effect on blueberry fruit quality traits

Comparison of two protective lung ventilatory regimes on oxygenation during one-lung ventilation: a randomized controlled trial

<p>Abstract</p> <p>Background</p> <p>The efficacy of protective ventilation in acute lung injury has validated its use in the operating room for patients undergoing thoracic surgery with one-lung ventilation (OLV). The purpose of this study was to investigate the effects of two different modes of ventilation using low tidal volumes: pressure controlled ventilation (PCV) vs. volume controlled ventilation (VCV) on oxygenation and airway pressures during OLV.</p> <p>Methods</p> <p>We studied 41 patients scheduled for thoracoscopy surgery. After initial two-lung ventilation with VCV patients were randomly assigned to one of two groups. In one group OLV was started with VCV (tidal volume 6 mL/kg, PEEP 5) and after 30 minutes ventilation was switched to PCV (inspiratory pressure to provide a tidal volume of 6 mL/kg, PEEP 5) for the same time period. In the second group, ventilation modes were performed in reverse order. Airway pressures and blood gases were obtained at the end of each ventilatory mode.</p> <p>Results</p> <p>PaO₂, PaCO₂and alveolar-arterial oxygen difference did not differ between PCV and VCV. Peak airway pressure was significantly lower in PCV compared with VCV (19.9 ± 3.8 cmH₂O vs 23.1 ± 4.3 cmH₂O; p < 0.001) without any significant differences in mean and plateau pressures.</p> <p>Conclusions</p> <p>In patients with good preoperative pulmonary function undergoing thoracoscopy surgery, the use of a protective lung ventilation strategy with VCV or PCV does not affect the oxygenation. PCV was associated with lower peak airway pressures.</p

Unconditionally converging multilinear operators

We introduce a notion of unconditionally converging multilinear operator which allows to extend many of the results of the linear case to the multilinear case. We prove several characterizations of these multilinear operators (one of which seems to be new also in the linear case), which allow to considerably simplify the work with this kind of operator

Some classes of multilinear operators on C(k) spaces

The authors obtain in this paper a classification of projective tensor products of C(K) spaces, in terms of the behaviour of certain classes of multilinear operators on the product of the spaces, or the verification of certain Banach space properties of the corresponding tensor product. The main tool used is an improvement of some results of Emmanuele and Hensgen on the reciprocal Dunford-Pettis and Pełczy´nski’s (V) properties of the projective tensor product of Banach spaces. Finally, the paper ends with a study of the relationships between some classes of multilinear operators and their linearizations

Polynomial convergence of sequences in Banach spaces.

Let E be a (complex) Banach space and n be a positive integer, and denote by P( n E) the space of all n -homogeneous polynomials on E . The authors say that E has the m -FJ property (m -Farmer-Johnson property) if, whenever (x n ) n is a sequence in E which converges weakly to x in E and P(x n ) converges to P(x) for all P∈P( m E) , then Q(x n ) converges to Q(x) for all Q∈P( k E) for all k , 1≤k≤m . If all m -homogeneous polynomials are weakly sequentially continuous, then E has the m -FJ property. Using this observation, the authors give an alternative proof of the result that if E is a Banach space such that every m -homogeneous polynomial on E is weakly continuous on bounded sets then every k -homogeneous polynomial, 1≤k≤m , is weakly continuous on bounded sets [C. Boyd and R. A. Ryan, Arch. Math. (Basel) 71 (1998), no. 3, 211–218;]. It is shown that the m -FJ property is equivalent to the condition that, whenever y∈E and (x n ) n is a sequence in E which converges weakly to x in E and moreover P(x n ) converges to P(x) for all P∈P( m E) , then P(x n +y) converges to P(x+y) for all P∈P( m E) . The main result of the paper is the following: Let E be a Banach space with an unconditional decomposition E=∑ ∞ k=1 E k . Suppose each E k is a Banach space such that, if (x n ) n is a sequence in E k with the property that whenever x n converges weakly to x and P(x n ) converges to P(x) for all P∈P( m E k ) , then x k converges in norm to x . Then E has the m -FJ property. If J denotes the James space, a corollary to the main theorem is that the space (∑⊗J) l p , 1≤p<∞ , has the m -FJ property for every integer m

Polynomial properties and symmetric tensor product of Banach spaces.

We study some classes of distinguished subsets of a Banach space in terms of polynomials and their relationship. This allows us to develop a systematic approach to study polynomial properties on a Banach space. We apply this approach to obtain several known and new results on the symmetric tensor product of a Banach space in a unified way