Annals of Functional Analysis最新文献

We give some characterizations of block dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space. We characterized the compactness of the finite sum of block dual Toeplitz products. Commuting block dual Toeplitz operators and quasinormal block dual Toeplitz operators are also considered.

Abstract

We characterize the good weights for some weighted weak-type iterated and bilinear modified Hardy inequalities to hold.

This paper describes the common properties of elements a and b satisfying (ab^n = b^{n + 1}) and (ba^n = a^{n + 1}) in the settings of Banach algebras, rings and operator algebras from the viewpoint of generalized inverses and spectral theory, where n is a positive integer. As applications, we show that if

are triangular operator matrices acting on the Banach space (X oplus X) such that (N_0, N_1) and (N_2) are nilpotent, then many subsets of the spectrum of (M_0) are the same with those of (M_1) and (M_2.) Moreover, we improve some recent extensions of Jacobson’s lemma and Cline’s formula for the Drazin inverse, generalized Drazin inverse and generalized Drazin–Riesz inverse.

In this paper, we give new bump conditions for two matrix weight inequalities of (L^{r})-Hörmander singular integral operators and rough singular integral operators, which are new even in the scalar cases. As applications, we obtain quantitative one weight inequalities for rough singular integral operators.

The concept of approximate oblique dual frame was introduced by Díaz, Heineken and Morillas. It is more general than traditional dual frame, oblique dual frame, and approximate dual frame. This paper addresses constructing more approximate oblique dual frame pairs starting from one given oblique dual frame pair. Using “analysis and synthesis operator”, “portrait”, and “gap” perturbation techniques, we present several sufficient conditions for constructing approximate oblique dual frame pairs under the general Hilbert space setting. As an application, we then focus on constructing approximate oblique dual frame pairs in shift-invariant subspaces of (L^{2}(mathbb R)).

In this paper, we study the composition operators (C_{varphi }) acting on the weighted Fock spaces (F^p_{alpha ,w}), where w is a weight satisfying some restricted (A_{infty })-conditions. We first characterize the boundedness and compactness of the composition operators (C_{varphi }:F^p_{alpha ,w}rightarrow F^q_{beta ,v}) for all (0<p,q<infty) in terms of certain Berezin type integral transforms. A new condition for the bounded embedding (I_d:F^p_{alpha ,w}rightarrow L^q(mathbb {C},mu )) in the case (p>q) is also obtained. Then, in the case that (w(z)=(1+|z|)^{mp}) for (min mathbb {R}), using some Taylor coefficient estimates, we establish an upper bound for the approximation numbers of composition operators acting on (F^p_{alpha ,w}).

Influenced by the concept of a p-compact operator due to Sinha and Karn (Stud Math 150(1): 17–33, 2002), we introduce p-compact Bloch maps of the open unit disk (mathbb {D}subseteq mathbb {C}) to a complex Banach space X, and obtain its most outstanding properties: surjective Banach ideal property, Möbius invariance, linearisation on the Bloch-free Banach space over (mathbb {D}), inclusion properties, factorisation of their derivatives, and transposition on the normalized Bloch space. We also present right p-nuclear Bloch maps of (mathbb {D}) to X and study its relation with p-compact Bloch maps.

This manuscript concerns with cyclic vectors in the Fock-type spaces ({L^{p}_{a}}(mathbb C^d,s,alpha )) of multi-variable cases, with positive parameters (s,alpha ) and (pge 1). The one-variable case has been settled by the authors. Here, it is shown that for a positive number (snot in mathbb {N}), a function f in the Fock-type space ({L^{p}_{a}}(mathbb C^d,s,alpha )) is cyclic if and only if f is non-vanishing. However, the case of s being a positive integer turns out to be more complicated. Different techniques and methods are developed in multi-variable cases for a complete characterization of cyclic vectors in ({L^{p}_{a}}(mathbb C^d,s,alpha )) for positive integers s.

Considering the deeper reasons of the appearance of a remarkable counterexample by Kaad and Skeide (J Operat Theory 89(2):343–348, 2023) we consider situations in which two Hilbert C*-modules (M subset N) with (M^bot = { 0 }) over a fixed C*-algebra A of coefficients cannot be separated by a non-trivial bounded A-linear functional (r_0: N rightarrow A) vanishing on M. In other words, the uniqueness of extensions of the zero functional from M to N is focussed. We show this uniqueness of extension for any such pairs of Hilbert C*-modules over W*-algebras, over monotone complete C*-algebras and over compact C*-algebras. Moreover, uniqueness of extension takes place also for any one-sided maximal modular ideal of any C*-algebra. Such a non-zero separating bounded A-linear functional (r_0) exist for a given pair of full Hilbert C*-modules (M subseteq N) over a given C*-algebra A iff there exists a bounded A-linear non-adjointable operator (T_0: N rightarrow N), such that the kernel of (T_0) is not biorthogonally closed w.r.t. N and contains M. This is a new perspective on properties of bounded modular operators that might appear in Hilbert C*-module theory. By the way, we find a correct proof of Lemma 2.4 of Frank (Int J Math 13:1–19, 2002) in the case of monotone complete and compact C*-algebras, but find it not valid in certain particular cases.

Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily prescribed portions of the gap as essential spectrum are identified and constructed within a general extension scheme. The emergence of new spectrum in the gap by self-adjoint extension is a problem with a long history and recent deep understanding, and yet it remains topical in several recent applications. Whereas it is already an established fact that, in case of infinite deficiency index, any kind of spectrum inside the gap can be generated by a suitable self-adjoint extension, the present discussion has the virtue of showing the clean and simple operator-theoretic mechanism of emergence of such extensions.