Banach Journal of Mathematical Analysis最新文献

In 2018, Oikhberg introduced and studied variants of the greedy and weak greedy algorithms for sequences with gaps, with a focus on the ({{textbf {n}}})-t-quasi-greedy property that is based on them. Building upon this foundation, our current work aims to further investigate these algorithms and bases while introducing new ideas for two primary purposes. First, we aim to prove that for ({{textbf {n}}}) with bounded quotient gaps, ({{textbf {n}}})-t-quasi-greedy bases are quasi-greedy bases. This generalization extends a previous result to the context of Markushevich bases and, also, completes the answer to a question by Oikhberg. The second objective is to extend certain approximation properties of the greedy algorithm to the context of sequences with gaps and study if there is a relationship between this new extension and the usual convergence.

We study the long-term behavior of solutions for stochastic delay p-Laplacian equation with multiplicative noise on unbounded thin domains. We first prove the existence and uniqueness of tempered random attractors for these equations defined on ((n+1))-dimensional unbounded thin domains. Then, the upper semicontinuity of these attractors when a family of ((n+1))-dimensional thin domains degenerates onto an n-dimensional domain as the thinness measure approaches zero is established.

The aim of the paper is to develop a general theory of solvability of linear inhomogeneous boundary-value problems for systems of ordinary differential equations of arbitrary order in Sobolev spaces. Boundary conditions are allowed to be overdetermined or underdetermined. They may contain derivatives, of the unknown vector-valued function, whose integer or fractional orders exceed the order of the differential equation. Similar problems arise naturally in various applications. The theory introduces the notion of a rectangular number characteristic matrix of the problem. The index and Fredholm numbers of this matrix coincide, respectively, with the index and Fredholm numbers of the inhomogeneous boundary-value problem. Unlike the index, the Fredholm numbers (i.e., the dimensions of the problem kernel and co-kernel) are unstable even with respect to small (in the norm) finite-dimensional perturbations. We give examples in which the characteristic matrix can be explicitly found. We also prove a limit theorem for a sequence of characteristic matrices. Specifically, it follows from this theorem that the Fredholm numbers of the problems under investigation are semicontinuous in the strong operator topology. Such a property ceases to be valid in the general case.

Let T be a bounded linear operator on a complex Hilbert space (mathcal {H}). We present some necessary and sufficient conditions for T to be the generalized pencil (P + alpha Q +beta PQ) of a pair (P, Q) of projections at some point ((alpha , beta )in mathbb {C}^2). The range and kernel relations of the generalized pencil T are studied and comments on the additional properties of some special generalized pencil are given.

This paper presents refined estimates for functional dual affine quermassintegrals, building upon the estimates of Dann et al. To sharpen the inequality, Dann et al. (Proc. Lond. Math. Soc. (3) 113(2):140–162, 2016) incorporated an (L^infty)-weight into the integration. We further refine these estimates and extend the (L^infty)-weight estimates to include a wider range of (L^{lambda })-weights where (lambda >1.)

The notion of p-summing Bloch mapping from the complex unit open disc (mathbb {D}) into a complex Banach space X is introduced for any (1le ple infty .) It is shown that the linear space of such mappings, equipped with a natural seminorm (pi ^{mathcal {B}}_p,) is Möbius-invariant. Moreover, its subspace consisting of all those mappings which preserve the zero is an injective Banach ideal of normalized Bloch mappings. Bloch versions of the Pietsch’s domination/factorization Theorem and the Maurey’s extrapolation Theorem are presented. We also introduce the spaces of X-valued Bloch molecules on (mathbb {D}) and identify the spaces of normalized p-summing Bloch mappings from (mathbb {D}) into (X^*) under the norm (pi ^{mathcal {B}}_p) with the duals of such spaces of molecules under the Bloch version of the (p^*)-Chevet–Saphar tensor norms (d_{p^*}.)

We study the boundedness of Hardy–Littlewood maximal function on the spaces defined in terms of Choquet integrals associated with weighted Bessel and Riesz capacities. As a consequence, we obtain a class of weighted Sobolev inequalities.

In this paper, we investigate some reflexivity-type properties of separable measurable Banach bundles over a (sigma )-finite measure space. Our two main results are the following:

• The fibers of a bundle are uniformly convex (with a common modulus of convexity) if and only if the space of its (L^p)-sections is uniformly convex for every (pin (1,infty )).

• The fibers of a bundle are reflexive if and only if the space of its (L^p)-sections is reflexive for every (pin (1,infty )).

They generalise well-known results for Lebesgue–Bochner spaces.

We study linear combinations of two composition operators induced by linear symbols on the Hilbert space of Dirichlet series. Based on partial reproducing kernels, we obtain an equivalent inscription of the compactness of a single composition operator and describe the compact linear combinations of composition operators.

Our focus is the operators of multivariable stochastic calculus, i.e., systems of transfer operators, covariance operators, conditional expectations, stochastic integrals, and the counterpart infinite-dimensional stochastic derivatives. In this paper, we present a new operator algebraic framework which serves to unify the analysis and the interrelations for the operators in question. Our approach uses Rokhlin decompositions, and it applies to both general classes of Gaussian processes, and white noise probability space, in commutative probability, as well as to the analogous operators in the framework of quantum (non-commutative) probability.