Related papers: Vector-valued numerical radius and $\sigma$-porosi…

It is proved that: each collectively order continuous set of operators from an Archimedean OVS with a generating cone to an OVS is collectively order bounded; and each collectively order to norm bounded set of operators from an ordered…

It is not usual to characterize an operator valued series via completeness of multiplier spaces. In this study, by using a series of bounded linear operators, we introduce the space $M^\infty_{R}\big(\sum_k T_k\big)$ of Riesz summability…

We prove that a bounded operator $T$ on a separable Banach space $X$ satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits…

We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of…

We consider the action of finitely truncated singular integral operators on functions taking values in a Banach space. Such operators are bounded for any Banach space, but we show a quantitative improvement over the trivial bound in any…

In this paper, we investigate the generalized numerical radius $\omega_N$, associated with a matrix norm $N$ defined by $\omega_N(X) = \sup_{\theta \in \mathbb{R}} N(\operatorname{Re}(e^{i\theta}X))$. We focus on matrices whose numerical…

We prove that for a given Banach space $X$, the subset of norm attaining Lipschitz functionals in $\mathrm{Lip}_0(X)$ is weakly dense but not strongly dense. Then we introduce a weaker concept of directional norm attainment and demonstrate…

Using the variational method, it is shown that the set of all strong peak functions in a closed algebra $A$ of $C_b(K)$ is dense if and only if the set of all strong peak points is a norming subset of $A$. As a corollary we can induce the…

Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…

If $\mu_1,\mu_2,\dots$ are positive measures on a measurable space $(X,\Sigma)$ and $v_1,v_2, \dots$ are elements of a Banach space ${\mathbb E}$ such that $\sum_{n=1}^\infty \|v_n\| \mu_n(X) < \infty$, then $\omega (S)= \sum_{n=1}^\infty…

The abscissas of convergence, uniform convergence and absolute convergence of vector valued Dirichlet series with respect to the original topology and with respect to the weak topology $\sigma(X,X')$ of a locally convex space $X$, in…

They proved several properties and introduced some inequalities. We continue with the study of this generalized numerical radius and we develop diverse inequalities involving w_N. We also study particular cases with a fixed N(.), for…

We investigate for a bounded semigroup of linear operators $S$ on a Banach space $E$ and a vector $x \in E$, when relative compactness of $S(I-T)x$ for every $T \in S$ implies relative compactness of the orbit $Sx$. In particular, we derive…

Employing the Orlicz functions we extend the Buzano's inequality which is a refinement of the Cauchy-Schwarz inequality. Also using the Orlicz functions we obtain several numerical radius inequalities for a bounded linear operator as well…

The classical Perron-Frobenius theory asserts that an irreducible matrix $A$ has cyclic peripheral spectrum and its spectral radius $r(A)$ is an eigenvalue corresponding to a positive eigenvector. In Radjavi (1999) and Radjavi and Rosenthal…

The Lipschitz space of an infinite (locally-finite) graph is defined as the set of functions on the vertices of the graph such that the differences of the values between adjacent vertices remain bounded. In this paper we prove that this set…

We study the Bishop-Phelps-Bollob\'as property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces ensuring the BPBp-nu. Among other results, we show that $L_1(\mu)$-spaces have this property for every…

We show that a bounded linear operator on a Banach space with closed range has range-kernel complementarity if and only if its generalized amplitude is less than $\pi$. An application to the strong convergence of the iterations of a bounded…

In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on…

The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by $\Sigma$, is defined. Some of the classical characterizations of this geometric notion for Banach spaces are studied in this new…