Related papers: O-frames for operators in Banach spaces

A bounded linear operator $T$ on a Banach space $X$ is called hypercyclic if there exists a vector $x \in X$ such that $orb{(x,T)}$ is dense in $X$. The Hypercyclicity Criterion is a well-known sufficient condition for an operator to be…

In this paper, we prove the following results. There exists a Banach space without basis which has a Schauder frame. There exists an universal Banach space $B$ (resp. $\tilde{B}$) with a basis (resp. an unconditional basis) such that, a…

We show that some previous results concerning the boundedness of differentiation and integration operators on weighted spaces given by radial weights in the unit disk or the complex plane might fail without some natural additional…

Let $H$ be a reflexive, dense, separable, infinite dimensional complex Hilbert space and let $B(H)$ be the algebra of all bounded linear operators on $H$. In this paper, we carry out characterizations of norm-attainable operators in normed…

We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…

In this note we extend two characterizations of admissible operators with respect to $\mathrm{L}^p$ to more general Orlicz spaces. The equivalent conditions are given by the property that an associated operator generates a strongly…

An operator $T$ on a Banach space is said to be of chain $N$ if there exist non-scalar operators $S_1,...,S_{N-1}$ and a non-zero compact $K$ such that $$T \leftrightarrow S_1 \leftrightarrow S_2 \leftrightarrow ...\leftrightarrow S_{N-1}…

We systematically derive general properties of continuous and holomorphic functions with values in closed operators, allowing in particular for operators with empty resolvent set. We provide criteria for a given operator-valued function to…

In this paper, we investigate the existence and uniqueness of fixed point for partially ordered contraction type operators in Banach Space. We also present applications to integral and differential equations.

Well-bounded operators are linear operators on a Banach space $X$ that have an $AC[a,b]$ functional calculus for some interval $[a,b]$. A well-bounded operator is of type (B) if it can be written as an integral against a spectral family of…

Resolvents of quasi-linear operators and operator algebras in Banach spaces over the quaternion field are investigated. Spectral theory of unbounded nonlinear operators in quaternion Banach spaces is studied. Strongly continuous semigroups…

Maz'ya and Shaposhnikova introduced a non-classical maximal operator $M^\diamond$ as the maximal convolution with the vector-valued signum kernel truncated to centered balls. We construct a translation-invariant Banach space of locally…

We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where…

If $X$ is a separable infinite dimensional Banach space, we construct a bounded and linear operator $R$ on $X$ such that $$ A_R=\{x \in X, \|R^tx\| \rightarrow \infty\} $$ is not dense and has non empty interior with the additional property…

We show that there are $2^{2^{\aleph_0}}$ different closed ideals in the Banach algebra $L(L_p(0,1))$, $1<p\not= 2<\infty$. This solves a problem in A. Pietsch's 1978 book "Operator Ideals". The proof is quite different from other methods…

The wark is a contribution to the functional calculus constructed by of the author and A. A. Atvinovskii of closed operators on Banach spaces. The calculus is based on Markov and related functions as symbols. Estimates of bounded…

We present a new programming paradigm which can be useful, in particular, for implementing window interfaces and parallel algorithms. This paradigm allows a user to define operators which can contain nested operators. The new paradigm is…

Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…

The main purpose of this note is to show that the question posed in the paper of Sinha D.P. and Karn A.K.("Compact operators which factor through subspaces of $l_p$ Math. Nachr. 281, 2008, 412-423; see the very end of that paper) has a…

In topological equivalence, a bounded linear operator between Banach spaces - we focus on the case of Hilbert spaces - is viewed as only acting linearly and continuously between them qua different spaces with the structure of linear…