Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces

[EN] Various dynamical properties of the differentiation and Volterra-type integral operators on generalized Fock spaces are studied. We show that the differentiation operator is always supercyclic on these spaces. We further characterize when it is hypercyclic, power bounded and uniformly mean ergodic. We prove that the operator satisfies the Ritt's resolvent condition if and only if it is power bounded and uniformly mean ergodic. Some similar results are obtained for the Volterra-type and Hardy integral operators.J. Bonet was partially supported by the research projects MTM2016-76647-P and GV Prometeo 2017/102 (Spain). M. Worku is supported by ISP project, Addis Ababa University, Ethiopia.Bonet Solves, JA.; Mengestie, T.; Worku, M. (2019). Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces. Results in Mathematics. 74(4):1-15. https://doi.org/10.1007/s00025-019-1123-7S115744Abanin, A.V., Tien, P.T.: Differentiation and integration operators on weighted Banach spaces of holomorphic functions. Math. Nachr. 290(8–9), 1144–1162 (2017)Atzmon, A., Brive, B.: Surjectivity and invariant subspaces of differential operators on weighted Bergman spaces of entire functions, Bergman spaces and related topics in complex analysis, Contemp. Math., vol. 404, Amer. Math. Soc., Providence, RI, pp. 27–39 (2006)Bayart, F., Matheron, E.: Dynamics of Linear Operators, Cambridge Tracts in Math, vol. 179. Cambridge Univ. Press, Cambridge (2009)Bermúdez, T., Bonilla, A., Peris, A.: On hypercyclicity and supercyclicity criteria. Bull. Austral. Math. Soc. 70, 45–54 (2004)Beltrán, M.J.: Dynamics of differentiation and integration operators on weighted space of entire functions. Studia Math. 221, 35–60 (2014)Beltrán, M.J., Bonet, J., Fernández, C.: Classical operators on weighted Banach spaces of entire functions. Proc. Am. Math. Soc. 141, 4293–4303 (2013)Bès, J., Peris, A.: Hereditarily hypercyclic operators. J. Funct. Anal. 167, 94–112 (1999)Bonet, J.: Dynamics of the differentiation operator on weighted spaces of entire functions. Math. Z. 26, 649–657 (2009)Bonet, J.: The spectrum of Volterra operators on weighted Banach spaces of entire functions. Q. J. Math. 66, 799–807 (2015)Bonet, J., Bonilla, A.: Chaos of the differentiation operator on weighted Banach spaces of entire functions. Complex Anal. Oper. Theory 7, 33–42 (2013)Bonet, J., Taskinen, J.: A note about Volterra operators on weighted Banach spaces of entire functions. Math. Nachr. 288, 1216–1225 (2015)Constantin, O., Persson, A.-M.: The spectrum of Volterra-type integration operators on generalized Fock spaces. Bull. Lond. Math. Soc. 47, 958–963 (2015)Constantin, O., Peláez, J.-Á.: Integral operators, embedding theorems and a Littlewood–Paley formula on weighted Fock spaces. J. Geom. Anal. 26, 1109–1154 (2016)De La Rosa, M., Read, C.: A hypercyclic operator whose direct sum is not hypercyclic. J. Oper. Theory 61, 369–380 (2009)Dunford, N.: Spectral theory. I. Convergence to projections. Trans. Am. Math. Soc. 54, 185–217 (1943)Grosse-Erdmann, K.G., Peris Manguillot, A.: Linear Chaos. Springer, New York (2011)Harutyunyan, A., Lusky, W.: On the boundedness of the differentiation operator between weighted spaces of holomorphic functions. Studia Math. 184, 233–247 (2008)Krengel, U.: Ergodic Theorems. Walter de Gruyter, Berlin (1985)Lyubich, Yu.: Spectral localization, power boundedness and invariant subspaces under Ritt’s type condition. Studia Mathematica 143(2), 153–167 (1999)Mengestie, T.: A note on the differential operator on generalized Fock spaces. J. Math. Anal. Appl. 458(2), 937–948 (2018)Mengestie, T.: Spectral properties of Volterra-type integral operators on Fock–Sobolev spaces. J. Kor. Math. Soc. 54(6), 1801–1816 (2017)Mengestie, T.: On the spectrum of volterra-type integral operators on Fock–Sobolev spaces. Complex Anal. Oper. Theory 11(6), 1451–1461 (2017)Mengestie, T., Ueki, S.: Integral, differential and multiplication operators on weighted Fock spaces. Complex Anal. Oper. Theory 13, 935–95 (2019)Mengestie, T., Worku, M.: Isolated and essentially isolated Volterra-type integral operators on generalized Fock spaces. Integr. Transf. Spec. Funct. 30, 41–54 (2019)Nagy, B., Zemanek, J.A.: A resolvent condition implying power boundedness. Studia Math. 134, 143–151 (1999)Nevanlinna, O.: Convergence of iterations for linear equations. Lecture Notes in Mathematics. ETH Zürich, Birkhäuser, Basel (1993)Ritt, R.K.: A condition that $$\lim _{n\rightarrow \infty } n^{-1}T^n =0$$. Proc. Am. Math. Soc. 4, 898–899 (1953)Ueki, S.: Characterization for Fock-type space via higher order derivatives and its application. Complex Anal. Oper. Theory 8, 1475–1486 (2014)Yosida, K.: Functional Analysis. Springer, Berlin (1978)Yosida, K., Kakutani, S.: Operator-theoretical treatment of Marko’s process and mean ergodic theorem. Ann. Math. 42(1), 188–228 (1941

TOI-1634 b: An Ultra-short-period Keystone Planet Sitting inside the M-dwarf Radius Valley

Studies of close-in planets orbiting M dwarfs have suggested that the M dwarf radius valley may be well-explained by distinct formation timescales between enveloped terrestrials, and rocky planets that form at late times in a gas-depleted environment. This scenario is at odds with the picture that close-in rocky planets form with a primordial gaseous envelope that is subsequently stripped away by some thermally-driven mass loss process. These two physical scenarios make unique predictions of the rocky/enveloped transition's dependence on orbital separation such that studying the compositions of planets within the M dwarf radius valley may be able to establish the dominant physics. Here, we present the discovery of one such keystone planet: the ultra-short period planet TOI-1634 b ($P=0.989$ days, $F=121 F_{\oplus}$, $r_p = 1.790^{+0.080}_{-0.081} R_{\oplus}$) orbiting a nearby M2 dwarf ($K_s=8.7$, $R_s=0.45 R_{\odot}$, $M_s=0.50 M_{\odot}$) and whose size and orbital period sit within the M dwarf radius valley. We confirm the TESS-discovered planet candidate using extensive ground-based follow-up campaigns, including a set of 32 precise radial velocity measurements from HARPS-N. We measure a planetary mass of $4.91^{+0.68}_{-0.70} M_{\oplus}$, which makes TOI-1634 b inconsistent with an Earth-like composition at $5.9\sigma$ and thus requires either an extended gaseous envelope, a large volatile-rich layer, or a rocky portion that is not dominated by iron and silicates to explain its mass and radius. The discovery that the bulk composition of TOI-1634 b is inconsistent with that of the Earth favors the gas-depleted formation mechanism to explain the emergence of the radius valley around M dwarfs with $M_s\lesssim 0.5 M_{\odot}$

Toi-1235 b: A keystone super-earth for testing radius valley emergence models around early m dwarfs

Small planets on close-in orbits tend to exhibit envelope mass fractions of either effectively zero or up to a few percent depending on their size and orbital period. Models of thermally-driven atmospheric mass loss and of terrestrial planet formation in a gas-poor environment make distinct predictions regarding the location of this rocky/non-rocky transition in period-radius space. Here we present the confirmation of TOI-1235 b ($P=3.44$ days, $r_p=1.738^{+0.087}_{-0.076}$ R$_{\oplus}$), a planet whose size and period are intermediate between the competing model predictions, thus making the system an important test case for emergence models of the rocky/non-rocky transition around early M dwarfs ($R_s=0.630\pm 0.015$ R$_{\odot}$, $M_s=0.640\pm 0.016$ M$_{\odot}$). We confirm the TESS planet discovery using reconnaissance spectroscopy, ground-based photometry, high-resolution imaging, and a set of 38 precise radial-velocities from HARPS-N and HIRES. We measure a planet mass of $6.91^{+0.75}_{-0.85}$ M$_{\oplus}$ which implies an iron core mass fraction of $20^{+15}_{-12}$% in the absence of a gaseous envelope. The bulk composition of TOI-1235 b is therefore consistent with being Earth-like and we constrain a H/He envelope mass fraction to be $<0.5$% at 90% confidence. Our results are consistent with model predictions from thermally-driven atmospheric mass loss but not with gas-poor formation, which suggests that the former class of processes remain efficient at sculpting close-in planets around early M dwarfs. Our RV analysis also reveals a strong periodicity close to the first harmonic of the photometrically-determined stellar rotation period that we treat as stellar activity, despite other lines of evidence favoring a planetary origin ($P=21.8^{+0.9}_{-0.8}$ days, $m_p\sin{i}=13.0^{+3.8}_{-5.3}$ M$_{\oplus}$) that cannot be firmly ruled out by our data

TOI-1634 b: An Ultra-short-period Keystone Planet Sitting inside the M-dwarf Radius Valley

Studies of close-in planets orbiting M dwarfs have suggested that the M dwarf radius valley may be well-explained by distinct formation timescales between enveloped terrestrials, and rocky planets that form at late times in a gas-depleted environment. This scenario is at odds with the picture that close-in rocky planets form with a primordial gaseous envelope that is subsequently stripped away by some thermally-driven mass loss process. These two physical scenarios make unique predictions of the rocky/enveloped transition's dependence on orbital separation such that studying the compositions of planets within the M dwarf radius valley may be able to establish the dominant physics. Here, we present the discovery of one such keystone planet: the ultra-short period planet TOI-1634 b ($P=0.989$ days, $F=121 F_{\oplus}$, $r_p = 1.790^{+0.080}_{-0.081} R_{\oplus}$) orbiting a nearby M2 dwarf ($K_s=8.7$, $R_s=0.45 R_{\odot}$, $M_s=0.50 M_{\odot}$) and whose size and orbital period sit within the M dwarf radius valley. We confirm the TESS-discovered planet candidate using extensive ground-based follow-up campaigns, including a set of 32 precise radial velocity measurements from HARPS-N. We measure a planetary mass of $4.91^{+0.68}_{-0.70} M_{\oplus}$, which makes TOI-1634 b inconsistent with an Earth-like composition at $5.9\sigma$ and thus requires either an extended gaseous envelope, a large volatile-rich layer, or a rocky portion that is not dominated by iron and silicates to explain its mass and radius. The discovery that the bulk composition of TOI-1634 b is inconsistent with that of the Earth favors the gas-depleted formation mechanism to explain the emergence of the radius valley around M dwarfs with $M_s\lesssim 0.5 M_{\odot}$

MLL-rearranged acute lymphoblastic leukemias activate BCL-2 through H3K79 methylation and are sensitive to the BCL-2-specific antagonist ABT-199

Targeted therapies designed to exploit specific molecular pathways in aggressive cancers are an exciting area of current research. Mixed Lineage Leukemia (MLL) mutations such as the t(4;11) translocation cause aggressive leukemias that are refractory to conventional treatment. The t(4;11) translocation produces an MLL/AF4 fusion protein that activates key target genes through both epigenetic and transcriptional elongation mechanisms. In this study, we show that t(4;11) patient cells express high levels of BCL-2 and are highly sensitive to treatment with the BCL-2-specific BH3 mimetic ABT-199. We demonstrate that MLL/AF4 specifically upregulates the BCL-2 gene but not other BCL-2 family members via DOT1L-mediated H3K79me2/3. We use this information to show that a t(4;11) cell line is sensitive to a combination of ABT-199 and DOT1L inhibitors. In addition, ABT-199 synergizes with standard induction-type therapy in a xenotransplant model, advocating for the introduction of ABT-199 into therapeutic regimens for MLL-rearranged leukemias

Toi-1235 b: A keystone super-earth for testing radius valley emergence models around early m dwarfs

Small planets on close-in orbits tend to exhibit envelope mass fractions of either effectively zero or up to a few percent depending on their size and orbital period. Models of thermally driven atmospheric mass loss and of terrestrial planet formation in a gas-poor environment make distinct predictions regarding the location of this rocky/nonrocky transition in period-radius space. Here we present the confirmation of TOI-1235 b (P = 3.44 days, rp1.738-0.076+0.087 R⊕), a planet whose size and period are intermediate between the competing model predictions, thus making the system an important test case for emergence models of the rocky/nonrocky transition around early M dwarfs (R s = 0.630± 0.015 ⊕, M s = 0.640 ± 0.016 ⊙. We confirm the TESS planet discovery using reconnaissance spectroscopy, ground-based photometry, high-resolution imaging, and a set of 38 precise radial velocities (RVs) from HARPS-N and HIRES. We measure a planet mass of 6.91-0.85+0.75M⊕ which implies an iron core mass fraction of 20-12+15% in the absence of a gaseous envelope. The bulk composition of TOI-1235 b is therefore consistent with being Earth-like, and we constrain an H/He envelope mass fraction to be &lt;0.5% at 90% confidence. Our results are consistent with model predictions from thermally driven atmospheric mass loss but not with gas-poor formation, suggesting that the former class of processes remains efficient at sculpting close-in planets around early M dwarfs. Our RV analysis also reveals a strong periodicity close to the first harmonic of the photometrically determined stellar rotation period that we treat as stellar activity, despite other lines of evidence favoring a planetary origin ( = P 21.8+0.9-0.8days,mp sin =13.0+ 3.8-5.3M⊕) that cannot be firmly ruled out by our data