Advances in Operator Theory最新文献

We investigate the essential norms of weighted composition operators and the differences of such operators acting between weighted Bergman spaces (mathcal {A}_{omega }^{p}), with a focus on almost standard radial weights. Motivated by the complexity of existing approaches that depend extensively on Carleson measures, we derive easily computable criteria for the compactness of weighted composition operators. Consequently, these criteria yield explicit estimates for the essential norms of such operators, and of their differences, including both lower and upper bounds, improving the best known bounds.

The aim of this paper is to study the two-sided remotely almost periodic solutions of ordinary differential equations in Banach spaces of the form (x'=A(t)x+f(t)+F(t,x)) with two-sided remotely almost periodic coefficients if the linear equation (x'=A(t)x) satisfies the condition of exponential trichotomy and nonlinearity F is "small".

We explore the procedure given by left-hand quotients in the context of weighted holomorphic ideals. On the one hand, we show that this procedure does not generate new ideals other than the ideal of weighted holomorphic mappings when considering the left-hand quotients induced by the ideals of p-compact, weakly p-compact, unconditionally p-compact, approximable or right p-nuclear operators with their respective weighted holomorphic ideals. On the other hand, the procedure is of interest when considering other operators ideals as it provides new weighted holomorphic ideals. This is the case of the ideal of Grothendieck weighted holomorphic mappings or the ideal of Rosenthal weighted holomorphic mappings, where the applicability of this construction is shown.

We analyze nonlocal Kirchhoff systems in fractional Musielak–Sobolev spaces. By means of Ricceri’s theorem, it is established that the system possesses weak solutions under fairly general conditions for the modular, the Kirchhoff functions, and the nonlinearities. Additionally, a case of growth of the logarithmic type is presented to visualize the outcome.

In this paper we study best m-term trigonometric approximation in weighted Wiener spaces and its consequences for Besov and Sobolev spaces with bounded mixed derivative/difference. We obtain several sharp asymptotic bounds for weighted Wiener spaces including the quasi-Banach case. It has recently been observed that best m-term trigonometric widths in the uniform norm together with recovery algorithms stemming from compressed sensing serve to control the optimal sampling recovery error in various relevant spaces of multivariate functions. We use a collection of old and new tools as well as novel findings to extend the recovery bounds to classical multivariate smoothness spaces. It turns out that embeddings into Wiener spaces serve as a powerful tool to improve certain recent bounds.

The main aim of this paper is to study Li–Yorke and Expansive composition operators on rearrangement-invariant Banach function spaces.

We consider a class of Markov interval maps (fin mathcal {M}(I)) with I an interval, whose associated transition matrix (A_f) is necessarily primitive. Then we search for subdynamics, i.e., a subset (Jsubset I) and (g=fvert _{J} in mathcal { M}([J])), with [J] the minimal closed interval containing J. The transition matrix (A_g) of g is obtained through successive state splittings of (A_f), followed by the removal of appropriate row(s) and column(s). We prove the existence of such J ensuring (gin mathcal {M}([J])). We also consider the Cuntz–Krieger algebra (mathcal {O}_{A_{f}}) representation (pi _{f,x}) on the Hilbert space associated to the f-orbit of each point (xin J). We similarly obtain a representation (pi _{g,x}) of (mathcal {O}_{A_{g}}). We prove that (pi _{g,x}(mathcal {O}_{A_{g}})) is a subalgebra of (pi _{f,x}(mathcal {O}_{A_{f}})). By exploring this further, we show that in fact (mathcal {O}_{A_{g}}) is a corner algebra of (mathcal {O}_{A_{f}}) by finding a projection (p_J) such that (mathcal {O}_{A_{g}}=p_{J},mathcal {O}_{A_{f}}p_{J}). We explicitly enumerate such corner algebras for each splitting state. This method provides a systematic way to construct concrete examples of specific Cuntz–Krieger corner algebras.

A unified approach to construct collections of K-spaces based on paramater couples with certain strong properties is formulated. This approach includes in particular the collections of K-spaces and small k-spaces.

Given a bounded positive linear operator A on a Hilbert space (mathcal {X}), this operator induces a semi-Hilbertian structure on (mathcal {X}). For a bounded linear operator T defined on the corresponding semi-Hilbertian space, we introduce a new definition of a Fredholm operator that is compatible with the semi-Hilbertian structure. Based on this definition, we proceed to define the essential spectra of T and establish their fundamental properties. Within this framework, we consider the bounded off-diagonal operator matrix (mathbb {T} = begin{pmatrix} 0 & M N & 0 end{pmatrix}) acting on the semi-Hilbertian space and demonstrate that the essential spectra of (mathbb {T}) are entirely determined by the essential spectra of the products MN and NM. Finally, an illustrative example is provided to substantiate the theoretical conclusions.

We prove some results concerning the finitely additive, vector integrals of Bochner and Pettis and their representation over a countably additive probability space. An application to the non compact Choquet theorem is also provided.