B. Duggal

activity

20082024

most citedStructure of elementary operators defining

m

-left invertible,

m

-selfadjoint and related classes of operators

17 citations · 44 across the 22 of their papers we have counts for

collaborators

23 papers

math.FA2024

Forms of biisometric operators and biorthogonality

B. P. Duggal, C. S. Kubrusly

The paper proves two results involving a pair (A,B) of P-biisometric or (m,P)-biisometric Hilbert-space operators for arbitrary positive integer m and positive operator P. It is sh…

math.FA2023

Weak l-sequential supercyclicity and weak quasistability

C. S. Kubrusly, B. P. Duggal

It is known that supercyclicity implies strong stability. It is not known whether weak l-sequential supercyclicity implies weak stability. In this paper we prove that weak l-sequen…

math.FA2023

On strict isometric and strict symmetric commuting $d$ -tuples of Banach space operators

B. P. Duggal

Given commuting $d$ -tuples $S_{i}$ and $T_{i}$ , $1 \leq i \leq 2$ , Banach space operators such that the tensor products pair $(\mathbb{S}_1\otimes\mathbb{S}_2,\mathbb{T…

math.FA2020

Expansive operators which are power bounded or algebraic

B. P. Duggal, I. H. Kim

Given Hilbert space operators $P, T \in B () ˝, P \geq 0$ invertible, $T$ is $(m, P) -$ expansive (resp., $(m, P) -$ isometric) for some positive integer $m$ if $\triangle_{T^*,T}^m(P)=\su…

math.FA2020

Operator roots of polynomials:iso-symmetric operators

B. P. Duggal, I. H. Kim

Given Hilbert space operators $A_{i}, B_{i}$ , $i = 1, 2$ , and $X$ such that $A_{1}$ commutes with $A_{2}$ and $B_{!}$ commutes with $B_{2}$ , and integers $m, n \geq 1$ , we say that the pairs of op…

math.FA2020★ 6 cited

Asymptotic limits, Banach limits, and Cesàro means

C. S. Kubrusly, B. P. Duggal

Every new inner product in a Hilbert space is obtained from the original one by means of a unique positive operator $.$ The first part of the paper is a survey on applications of su…

math.FA2020

Drazin invertible $(m, P)$ -expansive operators

B. P. Duggal, I. H. Kim

A Hilbert space operator $T \in B$ is $(m, P)$ -expansive, for some positive integer $m$ and operator $P \in B$ , if $\sum_{j=0}^m{(-1)^j\left(\begin{array}{clcr}m\\j\end{array}\right)T…

math.FA2020★ 14 cited

Structure of $n$ -quasi left $m$ -invertible and related classes of operators

B. P. Duggal, I. H. Kim

Given Hilbert space operators $T, S\in\B$, let $△$ and $δ\in B(\B)$ denote the elementary operators $△_{T, S} (X) = (L_{T} R_{S} - I) (X) = T X S - X$ and $δ_{T,S}(X)=(L_T-R_S)(X)=TX…

math.FA2020★ 17 cited

Structure of elementary operators defining $m$ -left invertible, $m$ -selfadjoint and related classes of operators

B. P. Duggal, I. H. Kim

We use elementary algebraic properties of left, right multiplication operators to prove some deep structural properties of left $m$ -invertible, $m$ -isometric, $m$ -selfadjoint and o…

math.FA2020★ 2 cited

Left m-invertibility by the adjoint of Drazin inverse and m-selfadjointness of Hilbert space operators

B. P. Duggal, I. H. Kim

A Hilbert space operator $A\in\B$ is left $(X, m)$ -invertible by $B\in\B$ (resp., $B\in\B$ is an $(X, m)$ -adjoint of $A\in\B$) for some operator $X\in\B$ if $\triangle_{B,A}^m(X)=\su…

math.FA2019★ 1 cited

On power Drazin normal and Drazin quasi-normal Hilbert space operators

B. P. Duggal, I. H. Kim

A Drazin invertible Hilbert space operator $T\in \B$, with Drazin inverse $T_{d}$ , is $(n, m)$ -power D-normal, $T \in [(n, m) D N]$ , if $[T_{d}^{n}, T^{* m}] = T_{d}^{n} T^{* m} - T^{* m} T_{d}^{n} = 0$ ; $T$ is…

math.FA2019

On $n$ th roots of normal operators

B. P. Duggal, I. H. Kim

For $n$ -normal operators $A$ [2, 4, 5], equivalently $n$ -th roots $A$ of normal Hilbert space operators, both $A$ and $A^{*}$ satisfy the Bishop--Eschmeier--Putinar property $(β)_{ε}$ ,…

math.SP2019

Generalized Drazin-meromorphic invertible operators and generalized Kato-meromorphic decomposition

Snežana Č. Živković-Zlatanović, Bhagwati P. Duggal

A bounded linear operator $T$ on a Banach space $X$ is said to be generalized Drazin-meromorphic invertible if there exists a bounded linear operator $S$ acting on $X$ such that $T…

math.FA2019★ 1 cited

Power bounded $m$ -left invertible operators

B. P. Duggal, C. S. Kubrusly

A Hilbert space operator $S\in\B$ is left $m$ -invertible by $T\in\B$ if $j = 0 \sum m (- 1)^{m - j} (m j) T^{j} S^{j} = 0,$ $S$ is $m$ -isometric if…

math.FA2018★ 1 cited

On n-quasi left m-invertible operators

B. P. Duggal

A Hilbert space operator $S\in\B$ is $n$ -quasi left $m$ -invertible (resp., left $m$ -invertible) by $T\in\B$, $m, n \geq 1$ some integers, if $S^{* n} p (S, T) S^{n} = 0$ (resp., $p (S, T) = 0$ ),…

math.FA2018

Isolated eigenvalues, poles and compact perturbations of Banach space operators

B. P. Duggal

Given a Banach space operator $A$ , the isolated eigenvalues $E (A)$ and the poles $Π (A)$ (resp., eigenvalues $E^{a} (A)$ which are isolated points of the approximate point spectrum and…

math.FA2018

On Weak Supercyclicity II

C. S. Kubrusly, B. P. Duggal

This paper considers weak supercyclicity for bounded linear operators on a normed space. On the one hand, weak supercyclicity is investigated for classes of Hilbert-space operators…

math.FA2018★ 1 cited

On Weak Supercyclicity I

C. S. Kubrusly, B. P. Duggal

This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak superc…

math.FA2015★ 1 cited

Compact perturbations and consequent hereditarily polaroid operators

B. P. Duggal

A Banach space operator $A \in B (X)$ is polaroid, $A \in P$ , if the isolated points of the spectrum $σ (A)$ are poles of the operator; $A$ is hereditarily polaroid, $A…

math.FA2014

Property (gw) for tensor product and left-right multiplication operators

Enrico Boasso, B. P. Duggal

Given Banach spaces $X$ and $Y$ and operators $A \in B (X)$ and $B \in B (Y)$ , property $(g w)$ does not in general transfer from $A$ and $B$ to the tensor product operator $A\otimes B\…

math.FA2013

Generalized Browder's and Weyl's theorems for left and right multiplication operators

Enrico Boasso, B. P. Duggal, I. H. Jeon

The main objective of this work is to study generalized Browder's and Weyl's theorems for the multiplication operators $L_{A}$ and $R_{B}$ and for the elementary operator $τ_{A,B}=L_AR…

math.FA2013

Generalized Browder's theorem for tensor product and elementary operators

Enrico Boasso, B. P. Duggal

The transfer property for the generalized Browder's theorem both of the tensor product and of the left-right multiplication operator will be characterized in terms of the $B$ -Weyl…

math.FA2008

Upper Triangular Operator Matrices, SVEP and Browder. Weyl Theorems

B. P. Duggal

A Banach space operator $T \in B (X)$ is polaroid if points $λ\in\isoσσ(T)$ are poles of the resolvent of $T$ . Let $σ_{a} (T)$ , $σ_{w} (T)$ , $σ_{a w} (T)$ , $σ_{S F_{+}} (T)$ and $σ_{SF_-}…

Forms of biisometric operators and biorthogonality

Weak l-sequential supercyclicity and weak quasistability

On strict isometric and strict symmetric commuting d-tuples of Banach space operators

Expansive operators which are power bounded or algebraic

Operator roots of polynomials:iso-symmetric operators

Asymptotic limits, Banach limits, and Cesàro means

Drazin invertible (m,P)-expansive operators

Structure of n-quasi left m-invertible and related classes of operators

Structure of elementary operators defining m-left invertible, m-selfadjoint and related classes of operators

Left m-invertibility by the adjoint of Drazin inverse and m-selfadjointness of Hilbert space operators

On power Drazin normal and Drazin quasi-normal Hilbert space operators

On nth roots of normal operators

Generalized Drazin-meromorphic invertible operators and generalized Kato-meromorphic decomposition

Power bounded m-left invertible operators

On n-quasi left m-invertible operators

Isolated eigenvalues, poles and compact perturbations of Banach space operators

On Weak Supercyclicity II

On Weak Supercyclicity I

Compact perturbations and consequent hereditarily polaroid operators

Property (gw) for tensor product and left-right multiplication operators

Generalized Browder's and Weyl's theorems for left and right multiplication operators

Generalized Browder's theorem for tensor product and elementary operators

Upper Triangular Operator Matrices, SVEP and Browder. Weyl Theorems

On strict isometric and strict symmetric commuting $d$ -tuples of Banach space operators

Drazin invertible $(m, P)$ -expansive operators

Structure of $n$ -quasi left $m$ -invertible and related classes of operators

Structure of elementary operators defining $m$ -left invertible, $m$ -selfadjoint and related classes of operators

On $n$ th roots of normal operators

Power bounded $m$ -left invertible operators