相关论文: Dynamics of weighted backward shifts on certain an…
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly…
We prove that the weighted quasi-Banach algebras of operator valued matrices satisfying Schur and Baskakov-Gohberg-Sj\"ostrand (BGS) conditions are inverse-closed in the Banach algebra $B(\ell^2(X,\mathcal{H}))$ whenever the weight is…
We extend a result of B\`{e}s, Martin, Peris and Shkarin by stating: $B_w$ is $\mathscr{F}$-weighted backward shift if and only if $(B_w,\dots, B_w^r)$ is $d$-$\mathscr{F}$, for any $r\in \mathbb{N}$, where $\mathscr{F}$ runs along some…
Functions in backward shift invariant subspaces have nice analytic continuation properties outside the spectrum of the inner function defining the space. Inside the spectrum of the inner function, Ahern and Clark showed that under some…
The Taylor (backward) shift on Bergman spaces $A^p(\om)$ for general open sets $\om$ in the extended complex plane shows rich variety concerning its dynamical behaviour. Different aspects are worked out, where in the case $p<2$ a recent…
We investigate Banach space automorphisms $T:\ell_\infty/c_0\rightarrow\ell_\infty/c_0 $ focusing on the possibility of representing their fragments of the form $$T_{B,A}:\ell_\infty(A)/c_0(A)\rightarrow \ell_\infty(B)/c_0(B)$$ for $A,…
We define positive Toeplitz operators between weighted harmonic Bloch spaces $b^\infty_\alpha$ on the unit ball of $\mathbb{R}^n$ for the full range of parameter $\alpha\in\mathbb{R}$. We give characterizations of bounded and compact…
We define positive Toeplitz operators between harmonic Bergman-Besov spaces $b^p_\alpha$ on the unit ball of $\mathbb{R}^n$ for the full ranges of parameters $0<p<\infty$, $\alpha\in\mathbb{R}$. We give characterizations of bounded and…
Recent results concerning the linear dynamics and mean ergodicity of compact operators in Banach spaces, together with additional new results, are employed to investigate various spectral properties of generalized Ces\`aro operators acting…
We extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fr\'echet sequence spaces.…
Rearrangement-invariance in function spaces can be viewed as a kind of generalization of 1-symmetry for Schauder bases. We define subrearrangement-invariance in function spaces as an analogous generalization of 1-subsymmetry. It is then…
In this paper, we define $A_{\vartheta _{1},\vartheta _{2}}^{p,1,q,r}\left(G\right) $ to be space of all functions in $\left( L_{\vartheta_{1}}^{p},\ell ^{1}\right) $ whose Fourier transforms belong to $\left( L_{\vartheta _{2}}^{q},\ell…
Some new characterizations on Carleson measures for weighted Bergman spaces on the unit ball involving product of functions are obtained. For these we characterize bounded and compact Toeplitz operators between weighted Bergman spaces. The…
We study positive Toeplitz operators on the Bergman spaces having the fast decreasing weight functions in a certain class. We give the characterizations for the boundedness and compactness of Toeplitz operators in terms of their Berezin…
We consider the Buhmann class of compactly supported radial basis functions, whih includes a wealth of special cases that have been studied in both numerical analysis and spatial statistics literatures. In particular, the celebrated Wu,…
We show that every subsymmetric Schauder basis $(e_j)$ of a Banach space $X$ has the factorization property, i.e. $I_X$ factors through every bounded operator $T\colon X\to X$ with a $\delta$-large diagonal (that is $\inf_j |\langle Te_j,…
We introduce $B_w^u$-function spaces which unify Lebesgue, Morrey-Campanato, Lipschitz, $B^p$, CMO, local Morrey-type spaces, etc., and investigate the interpolation property of $B_w^u$-function spaces. We also apply it to the boundedness…
In this paper we will show how the boundedness condition for the weighted composition operators on a class of spaces of analytic functions on the open right complex half-plane called Zen spaces (which include the Hardy spaces and weighted…
For any $p\in[1,\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in B\"ochner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With…
We prove that the spaces $\ell_p$, $1<p<\infty, p\ne 2$, and all infinite-dimensional subspaces of their quotient spaces do not admit equivalent almost transitive renormings. This is a step towards the solution of the Banach-Mazur rotation…