Advances in Operator Theory最新文献

Let (mathbb {H}_d:=mathbb {C}^dtimes mathbb {R},) ((din mathbb {N}^*)) be the (2d+1)-dimensional Heisenberg group and we denote by U(d) (the unitary group) the maximal compact connected subgroup of (Aut(mathbb {H}_d),) the group of automorphisms of (mathbb {H}_d.) Let (G_d:=U(d) < imes mathbb {H}_d) be the Heisenberg motion group. In this work, we describe the (C^*)-algebra (C^*(G_d),) of (G_d) in terms of an algebra of operator fields defined over its dual space (widehat{G_d}.) This result generalizes a previous result in Ludwig and Regeiba (Complex Anal Oper Theory 13(8):3943–3978, 2019).

In this paper, we study the approximate minimizing property (AMp) for operators, a localized Bishop-Phelps-Bollobás type property with respect to the minimum norm. Given Banach spaces X and Y we define a new class (mathcal{A}mathcal{M}(X,Y)) of bounded linear operators from X to Y for which the pair (X, Y) satisfies the AMp. We provide a necessary and sufficient condition for non-injective operators from X to Y to be in the class (mathcal{A}mathcal{M}(X,Y)). We also prove that X is finite dimensional if and only if for every Banach space Y, (X, Y) has the AMp for all minimum norm attaining operators from X to Y if and only if for every Banach space Y, (Y, X) has the AMp for all minimum norm attaining operators from Y to X. We also study the AMp with respect to Crawford number called AMp-c for operators.

The aim of the present paper is the investigation of matrix singular integral operators with reflection in Lebesgue spaces on the real line with Muckenhoupt weights. It is proved that these operators are matrix coupled with matrix Toeplitz operators. As a corollary, a criterion for the Fredholmness of such operators with piecewise continuous coefficients is obtained. Singular integral operators with flip and Toeplitz plus Hankel operators are also considered.

We present some weighted norm inequalities of bounded adjointable operators on the Hilbert C*-modules. Further, we use the Cartesian decomposition to obtain the lower bounds of numerical radius inequality over Hilbert C*-module. And the existing inequalities of numerical radius on the Hilbert C*-modules are refined.

Sequences defining a weighted matrix geometric mean are investigated and their convergence speed is analyzed. The superlinear convergence of a weighted mean based on the Ando–Li–Mathias (ALM) construction is proved. A weighted Cheap mean is defined and conditions on the weights for linear or superlinear convergence of order at least three are provided.

In the paper we introduce new norm derivative mappings and the corresponding orthogonality relations induced by it. We show that this notion is useful in the characterization of inner product spaces, characterization of smooth Banach spaces, Birkhoff orthogonality. We prove also some useful computational formulations.

In this paper two classes of operators related to weakly p-compact and almost Dunford–Pettis sequences which will be called almost Dunford–Pettis p-convergent operators and weak almost p-convergent operators are studied. Some properties of Banach lattices, the weak Dunford–Pettis property of order p and the strong relatively compact Dunford–Pettis property of order p are characterized in terms of almost Dunford–Pettis p-convergent and weak almost p-convergent operators.

The aim of the paper is to characterize all quasi-parabolic operators and provide an integral representation to each quasi-parabolic operator on the Bergman space (A_{lambda }^2(D_n)). We explore some aspects of operator theoretic properties such as compactness, spectrum, common invariant subspaces and more. Further, we show that the collection of all quasi-parabolic operators forms a maximal commutative (C^*)-algebra. As a consequence, we provide integral representation for operators in the (C^*)-algebra generated by Toeplitz operators with essentially bounded quasi-parabolic defining symbols.

We study weakly compact multilinear operators. We prove a variant of Gantmacher’s weak compactness theorem for multilinear operators. We also present Lions–Peetre type results on weak compactness interpolation for multilinear operators. Furthermore, we provide an analogue of Persson’s result on interpolation of weakly compact operators under the assumption that the target Banach couple satisfies a certain weakly compact approximation property.

In the present paper, based on the so called degree of nondensifiability (DND), we introduce the concept of Banach–Mazur nondensifiability number of two given Banach spaces and prove that such a number is an optimal lower bound for the well known Banach–Mazur distance. For a given infinite dimensional Banach space, we also introduce a new constant. We demonstrate a relationship between this constant and the Banach–Mazur distance.