Related papers: The Ritt property of subordinated operators in the…

Let $G$ be a locally compact group and $\mu$ a probability measure on $G,$ which is not assumed to be absolutely continuous with respect to Haar measure. Given a unitary representation $(\pi, \cal H)$ of $G,$ we study spectral properties of…

In this article, we develop a framework for the joint functional calculus of commuting pair of $\text{Ritt}_{\text{E}}$ operators on Banach spaces. We establish a transfer principle that relates the bounded holomorphic functional calculus…

Let $X$ be a separable Banach space and let $Q:X^*\rightarrow X$ be a linear, bounded, non-negative and symmetric operator and let $A:D(A)\subseteq X\rightarrow X$ be the infinitesimal generator of a strongly continuous semigroup of…

This paper is devoted to the multivariable $H^\infty$ functional calculus associated with a finite commuting family of sectorial operators on Banach space. First we prove that if $(A_1,\ldots, A_d)$ is such a family, if $A_k$ is…

For a subset $E = \{\xi_1, ..., \xi_N\}$ of the unit circle $\mathbb{T}$, the notion of Ritt$_E$ operators on a Banach space and their functional calculus on generalized Stolz domains was developed and studied in arXiv:2203.05373. In this…

Let X be a complex Banach space of dimension at least 2, and let S be a multiplicative semigroup of operators on X such that the rank of AB - BA is at most 1 for all pairs {A,B} in S. We prove that S has a non-trivial invariant subspace…

In this paper, we study geometric properties of the set of group invariant continuous linear operators between Banach spaces. In particular, we present group invariant versions of the Hahn-Banach separation theorems and elementary…

We study the coefficients of the Taylor series expansion of powers of the function $\psi(x)=\frac{1-\sqrt{1-x}}{x}$, where the Brunel operator $A\equiv A(T)$ is defined as $\psi(T)$ for any mean-bounded $T$. We prove several new precise…

Generalizing the notion of numerical range and numerical radius of an operator on a Banach space, we introduce the notion of joint numerical range and joint numerical radius of tuple of operators on a Banach space. We study the convexity of…

Suppose $X$ and $Y$ are Banach spaces, $K$ is a compact Hausdorff space, $\Sigma$ is the $\sigma$-algebra of Borel subsets of $K$, $C(K,X)$ is the Banach space of all continuous $X$-valued functions (with the supremum norm), and…

Averaged operators have played an important role in fixed point theory in Hilbert spaces. They emerged as a necessity to obtain solutions to fixed point problems where the underlying operator is not contractive and thus renders Banach fixed…

We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…

We investigate the space of bounded linear operators on a Banach space equipped with a norm which is equivalent to the operator norm such that the subspace of compact operators is an M-ideal. In particular, we observe that the space of…

In this article, the class of all Dunford-Pettis $ p $-convergent operators and $ p $-Dunford-Pettis relatively compact property on Banach spaces are investigated. Moreover, we give some conditions on Banach spaces $ X $ and $ Y $ such that…

This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…

Given $N\ge2$ closed subspaces $M_1,\dotsc, M_N$ of a Hilbert space $X$, let $P_k$ denote the orthogonal projection onto $M_k$, $1\le k\le N$. It is known that the sequence $(x_n)$, defined recursively by $x_0=x$ and $x_{n+1}=P_N\cdots…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if…

The numerical range of a bounded linear operator on a complex Banach space need not be convex unlike that on a Hilbert space. The aim of this paper is to study operators $T$ on $ \ell^2_p $ for which the numerical range is convex. We also…

Let G be a locally compact abelian group and let \mu be a complex valued regular Borel measure on G. In this paper we consider a generalisation of a class of Banach lattices introduced in [6]. We use Laplace transform methods to show that…