Annals of Functional Analysis最新文献

In this paper, we present a version of the Schur inequality in the setting of Murray–von Neumann algebras, extending a result by Arveson and Kadison. We also describe the ring isomorphisms between (*)-subalgebras of two Murray–von Neumann algebras. A short proof of the commutator estimation theorem for Murray–von Neumann algebras is given as an easy application.

In this paper, we are concerned with the various properties of the Toeplitz operators acting on the Dirichlet spaces. First, we consider the matrix representation of Toeplitz operators with harmonic and monomial symbols. Second, we establish the expansivity and contractivity of the Toeplitz operators (T_{varphi }) with monomial symbols (varphi ). Third, we give a necessary and sufficient conditions for the normality and hyponormality of the Toeplitz operators (T_{varphi }) with such symbols on the Dirichlet spaces.

We prove that a normalised linear functional on certain symmetric spaces associated with a semifinite von Neumann algebra, respects tail majorisation if and only if it is a Dixmier-type trace.

Due to the frame elements of the g-frames being operators, it has many differences from traditional frames. Hence some new characterizations of exact phase-retrievable g-frames from the perspective of operator theory are mainly discussed in this paper. Firstly, we find that for an exact phase-retrievable g-frame, its canonical dual frame will maintain the exact phase-retrievability. Then the stability of the exact phase-retrievability is discussed. More specifically, an exact phase-retrievable g-frame is still exact phase-retrievable after a small disturbance can be obtained in this paper. In addition, we show that the direct sum of two g-frames which have the exact PR-redundancy property also have the exact PR-redundancy property. With the help of these results, the existence of the exact phase-retrievable g-frames is discussed. We prove that for the real Hilbert space case, an exact phase-retrievable g-frame of length N exists for every (2n-1le N le frac{n(n+1)}{2}.)

In this paper, we study Choquard systems with linear and nonlinear couplings with different potentials under the (L^2)-constraint. We use Ekland variational principle to prove this system has a normalized radially symmetric solution for (L^2)-subcritical case when the dimension is greater than or equal to 2 without potentials. In addition, a positive solution with prescribed (L^2)-constraint under some appropriate assumptions with the potentials was obtained. The proof is based on the refined energy estimates.

In this paper, we study decomposability for sums of complex symmetric operators. As applications, we consider decomposable operator matrices.

The main purpose of this paper is to investigate the converse problems of some well-known results related to the generalized Drazin (g-Drazin for short) inverse in Banach algebras. Let ({mathcal {A}}) be a Banach algebra and (a,bin {mathcal {A}}). First, we give the relationship between the Drazin (g-Drazin, group) invertibility of a, b and that of the sum (a+b) under certain conditions. Then, for a given polynomial (f(x)in {mathbb {C}}[x]), the g-Drazin invertibility of f(a), (f(a^{d})), f(ab), (f(1-ab)) and (f(a+b)) are investigated.

Let ({mathcal {A}}) be a unital JB-algebra and (A,Bin {mathcal {A}}). The weighted geometric mean (Asharp _r B) for (A,Bin {mathcal {A}}) has been recently defined for (rin [0,1].) In this work, we extend the weighted geometric mean (Asharp _r B), from (rin [0,1]) to (rin (-1, 0)cup (1, 2)). We will notice that many results will be reversed when the domain of r change from [0, 1] to ((-1,0)) or (1, 2). We also introduce the Heinz and Heron means of elements in ({mathcal {A}}), and extend some known inequalities involving them.

This article is devoted to introduce a new geometric constant called Dehghan–Rooin constant, which quantifies the difference between angular and skew angular distances in Banach spaces. We quantify the characterization of uniform non-squareness in terms of Dehghan–Rooin constant. The relationships between Dehghan–Rooin constant and uniform convexity, Dehghan-Rooin constant and uniform smoothness are also studied. Moreover, some new sufficient conditions for uniform normal structure are also established in terms of Dehghan–Rooin constant.

The main goal of this paper is to discuss the local Hölder continuity of the gradients for weak solutions of the following non-homogenous elliptic p(x)-Laplacian equations of divergence form

where (Omega subset mathbb {R}^{n}) is an open bounded domain for (n ge 2), under some proper non-Hölder conditions on the variable exponents p(x) and the coefficients matrix A(x).