1,865 research outputs found
Overcomplete sets in non-separable Banach spaces
We introduce and study the notion of overcomplete set in a Banach space, that
subsumes and extends the classical concept of overcomplete sequence in a
(separable) Banach space. We give existence and non-existence results of
overcomplete sets for a wide class of (non-separable) Banach spaces and we
study to which extent properties of overcomplete sequences are retained by
every overcomplete set
Banach spaces of continuous functions without norming Markushevich bases
We investigate the question whether a scattered compact topological space
such that has a norming Markushevich basis (M-basis, for short) must be
Eberlein. This question originates from the recent solution, due to H\'ajek,
Todor\v{c}evi\'c, and the authors, to an open problem from the Nineties, due to
Godefroy. Our prime tool consists in proving that does not
embed in a Banach space with a norming M-basis, thereby generalising a result
due to Alexandrov and Plichko. Subsequently, we give sufficient conditions on a
compact for not to embed in a Banach space with a norming M-basis.
Examples of such conditions are that is a -dimensional compact space
with a P-point, or a compact tree of height at least . In
particular, this allows us to answer the said question in the case when is
a tree and to obtain a rather general result for Valdivia compacta. Finally, we
give some structural results for scattered compact trees; in particular, we
prove that scattered trees of height less than are Valdivia
A combination of tryptophan, Satureja montana, Tribulus terrestris, Phyllanthus emblica extracts is able to improve sexual quality of life in patient with premature ejaculation
Objective: The management of patient affected by premature ejaculation (PE) is nowadays not highly satisfactory. Here, we aimed to evaluate the tolerability and efficacy of a combination of tryptophan, Satureja montana, Tribulus terrestris, Phyllanthus emblica extracts in order to improve sexual quality of life in patients with premature ejaculation. Materials and methods: All patients attending to 5 urological centers from January 2015 to March 2015, due to premature ejaculation were enrolled in this study. At the enrolment visit, all subjects underwent self-administered IIEF-5, Male Sexual Health Questionnaire-Ejaculation Disorder (MSHQ-EjD), PEDT and IELTS (calculated as mean from that perceived by partner and that perceived by patient) and underwent urological visit and laboratory examinations. All patients received one tablet per day of a combination of tryptophan, Satureja montana, Tribulus terrestris, Phyllanthus emblica extracts for 3 months (Group A). After 3 months all patients underwent follow-up visit with the same investigations that have been carried out in the enrolment visit. The results were compared with a cohort of patients enrolled in the same period in another urological center and considered as a control group (Group B). All patients in the control group underwent counseling and sexual behavioral treatment without any pharmacological compound. Results: At the follow-up analysis, significant changes in terms of IELT in the Group A (mean difference: 31.90; p < 0.05) at 3 months and versus Group B at the intergroup analysis (mean difference: 30.30; p < 0.05) were reported. In the group A, significant differences from baseline to last follow-up were observed relative to IIEF-5 (mean difference: 1.04; p < 0.05), PEDT (mean difference: -2.57; p < 0.05) and FSH (mean difference: -16.46; p < 0.05). Conclusion: In conclusion, patients affected by PE may significantly benefit from oral therapy with a combination of tryptophan, Satureja montana, Tribulus terrestris, Phyllanthus emblica extracts in terms of IELT and PEDT scores improvement
Separated sets and Auerbach systems in Banach spaces
The paper elucidates the relationship between the density of a Banach space
and possible sizes of well-separated subsets of its unit sphere. For example,
it is proved that for a large enough space , the unit sphere always
contains an uncountable -separated subset. In order to achieve this, new
results concerning the existence of large Auerbach systems are established that
happen to be sharp for the class of WLD spaces. In fact, we offer the first
consistent example of a non-separable WLD Banach space that contains no
uncountable Auerbach system, as witnessed by a renorming of .
Moreover, the following optimal results for the classes of, respectively,
reflexive and super-reflexive spaces are established: the unit sphere of an
infinite-dimensional reflexive space contains a symmetrically
-separated subset of any regular cardinality not exceeding the
density of ; should the space be super-reflexive, the unit sphere of
contains such a subset of cardinality equal to the density of . The said
problem is studied for other classes of spaces too, including the RNP spaces or
strictly convex ones.Comment: 39 pp, Trans. Amer. Math. Soc. (in press
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