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881.
《Indagationes Mathematicae》2017,28(3):670-679
In this paper, we use the concept of quasi-compact operators, as a generalization of the class of Riesz operators, to improve the definition of the pseudo-Schechter essential spectrum of a closed densely defined operator acting on Banach space. Moreover, we discuss the incidence of some perturbation results on the behavior of pseudo-essential spectra of the sum of two bounded linear operators. 相似文献
882.
《Mathematische Nachrichten》2017,290(1):37-49
We prove that Burenkov's extension operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n‐dimensional Euclidean space. 相似文献
883.
《Mathematische Nachrichten》2017,290(4):507-519
We show a picture of the relations among different types of summability of series in the space of integrable functions with respect to a vector measure m of relatively norm compact range. In order to do that, we study the class of the so‐called m‐1‐summing operators. We give several applications regarding the existence of copies of c 0 in , as well as on m‐1‐summing operators which are weakly compact, Asplund or weakly precompact. 相似文献
884.
《Mathematische Nachrichten》2017,290(16):2560-2566
In this paper, we describe a second main theorem of holomorphic curves in , of hyper‐order strictly less than 1, that involves a general linear operator . As an application, we derive a truncated second main theorem of degenerate holomorphic curves of hyper‐order strictly less than 1 using Nochka weights. 相似文献
885.
《Mathematische Nachrichten》2017,290(14-15):2388-2400
In this paper, we study the high‐dimensional Hausdorff type operators and establish their boundedness on the power weighted Hardy spaces for . As a consequence, we obtain that the Hausdorff type operator is bounded on if Φ is the Gauss function, or the Poisson function. 相似文献
886.
《Mathematische Nachrichten》2017,290(11-12):1732-1752
This paper provides various “contractivity” results for linear operators of the form where C are positive contractions on real ordered Banach spaces X . If A generates a positive contraction semigroup in Lebesgue spaces , we show (M. Pierre's result) that is a “contraction on the positive cone ”, i.e. for all provided that . We show also that this result is not true for 1 ⩽ . We give an extension of M. Pierre's result to general ordered Banach spaces X under a suitable uniform monotony assumption on the duality map on the positive cone . We deduce from this result that, in such spaces, is a contraction on for any positive projection C with norm 1. We give also a direct proof (by E. Ricard) of this last result if additionally the norm is smooth on the positive cone. For any positive contraction C on base‐norm spaces X (e.g. in real spaces or in preduals of hermitian part of von Neumann algebras), we show that for all where N is the canonical half‐norm in X . For any positive contraction C on order‐unit spaces X (e.g. on the hermitian part of a algebra), we show that is a contraction on . Applications to relative operator bounds, ergodic projections and conditional expectations are given. 相似文献
887.
《Mathematische Nachrichten》2017,290(17-18):2788-2799
A well‐known result of J. Lindenstrauss and A. Pełczyński (1968) gives the existence of a universal non‐weakly compact operator between Banach spaces. We show the existence of universal non‐Rosenthal, non‐limited, and non‐Grothendieck operators. We also prove that there does not exist a universal non‐Dunford–Pettis operator, but there is a universal class of non‐Dunford–Pettis operators. Moreover, we show that, for several classes of polynomials between Banach spaces, including the non‐weakly compact polynomials, there does not exist a universal polynomial. 相似文献
888.
Lisun Zheng 《代数通讯》2017,45(6):2417-2434
889.
We consider a linear parabolic problem in a thick junction domain which is the union of a fixed domain and a collection of periodic branched trees of height of order 1 and small width connected on a part of the boundary. We consider a three‐branched structure, but the analysis can be extended to n‐branched structures. We use unfolding operator to study the asymptotic behavior of the solution of the problem. In the limit problem, we get a multi‐sheeted function in which each sheet is the limit of restriction of the solution to various branches of the domain. Homogenization of an optimal control problem posed on the above setting is also investigated. One of the novelty of the paper is the characterization of the optimal control via the appropriately defined unfolding operators. Finally, we obtain the limit of the optimal control problem. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
890.
Lin Feng Wang Ze Yu Zhang Liang Zhao Yu Jie Zhou 《Mathematical Methods in the Applied Sciences》2017,40(4):992-1002
We prove that on a smooth metric measure space with m ?Bakry–Émery curvature bounded from below by ?(m ? 1)K for some constant K ≥0 (i.e., Ricf ,m ≥?(m ? 1)K ), the following degenerate elliptic equation (0.1) has no nonconstant positive solution when p > 1 and constant λ f ,p satisfies Our approach is based on the local Sobolev inequality and the Moser's iterative technique and is different from Cheng‐Yau's method, which was used by Wang‐Zhu in 2012 to derive a same Liouville theorem when 1 < p ≤2, Ricf ,m ≥?(m ? 1)K and the sectional curvature is bounded from below. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献