Annals of Functional Analysis最新文献

Let (mathbb {D}) denote the unit disc in (mathbb {C}). We define the generalized Cesàro operator as follows:

where ({B^{omega }_zeta }_{zeta in mathbb {D}}) are the reproducing kernels of the Bergman space (A^{2}_{omega }) induced by a radial weight (omega ) in the unit disc (mathbb {D}). We study the action of the operator (C_{omega }) on weighted Hardy spaces of analytic functions (mathcal {H}_{gamma }), (gamma >0) and on general weighted Bergman spaces (A^{2}_{mu }).

In 1953, Grothendieck introduced and studied the Dunford–Pettis property (the ({textrm{DP}}) property) and the strict Dunford–Pettis property (the strict ({textrm{DP}}) property). The ({textrm{DP}}) property of order (pin [1,infty ]) for Banach spaces was introduced by Castillo and Sanchez in 1993. Being motivated by these notions, for (p,qin [1,infty ],) we define the quasi-Dunford–Pettis property of order p (the quasi ({textrm{DP}}_p) property) and the sequential Dunford–Pettis property of order (p, q) (the sequential ({textrm{DP}}_{(p,q)}) property). We show that a locally convex space (lcs) E has the ({textrm{DP}}) property if the space E endowed with the Grothendieck topology (tau _{Sigma '}) has the weak Glicksberg property, and E has the quasi ({textrm{DP}}_p) property if the space ((E,tau _{Sigma '}) ) has the p-Schur property. We also characterize lcs with the sequential ({textrm{DP}}_{(p,q)}) property. Some permanent properties and relationships between Dunford–Pettis type properties are studied. Numerous (counter)examples are given. In particular, we give the first example of an lcs with the strict ({textrm{DP}}) property but without the ({textrm{DP}}) property and show that the completion of even normed spaces with the ({textrm{DP}}) property may not have the ({textrm{DP}}) property.

Given an infinite matrix (M=(m_{nk})), we study a family of sequence spaces (ell _M^p) associated with it. When equipped with a suitable norm (Vert cdot Vert _{M,p}), we prove some basic properties of the Banach spaces of sequences ((ell _M^p,Vert cdot Vert _{M,p})). In particular, we show that such spaces are separable and strictly/uniformly convex for a considerably large class of infinite matrices M for all (p>1). A special attention is given to the identification of the dual space ((ell _M^p )^*). Building on the earlier works of Bennett and Jägers, we extend and apply some classical factorization results to the sequence spaces (ell _M^p).

We investigate the geometric properties for a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. We extend earlier results of Epstein, Hiai, Carlen and Lieb.

We introduce the C-decomposition property for reducible bounded linear operators on a Hilbert space, and prove that an arbitrary idempotent operator has the C-decomposition property with respect to a particular space decomposition, which is related to Halmos’ two projections theory. Using this, we obtain a general explicit description for all the conjugations C such that a given idempotent operator is a C-projection. We also present a characterization of the ranges of C-projections for any conjugation C.

Let (0<alpha <1). We obtain necessary and sufficient conditions for the boundedness of the discrete fractional Hardy–Littlewood maximal operators (mathcal {M}_alpha ) on discrete weighted Lebesgue spaces. From this and a discrete variant of the Whitney decomposition theorem, necessary and sufficient conditions for the boundedness of the discrete Riesz potentials (I_alpha ) on discrete weighted Lebesgue spaces are discussed. As an application, the boundedness of (I_alpha ) on discrete weighted Morrey spaces is further obtained.

In this paper, we first completely characterize the complex symmetric Toeplitz operators (T_varphi ) on the Hardy spaces (H^2({mathbb {D}})) with conjugations ({mathcal {C}}_p^{i,j}) and ({mathcal {C}}_n). Next, we give a method to determine the coefficients of (varphi (z)) when (T_varphi ) is complex symmetric on (H^2({mathbb {D}})) with the conjugation ({mathcal {C}}_sigma ), which partially solves a problem raised by [2]. Finally, we consider the complex symmetric Toeplitz operators (T_varphi ) on the weighted Bergman spaces (A^2({mathbb {B}}_{n})) and the pluriharmonic Bergman spaces (b^2({mathbb {B}}_{n})) with conjugations ({mathcal {C}}_V), where V is a symmetric permutation matrix.

We explore functors between operator space categories, some properties of these functors, and establish relations between objects in these categories and their images under these functors, in particular regarding injectivity and injective envelopes. We also compare the purely categorical definition of injectivity with the ‘standard’ operator theoretical definition. An appendix by D. P. Blecher discusses the unitization of an operator space and its injective envelope.