Arup Majumdar

collaborators

4 papers

math.FA2024

On the generalized Cauchy dual of closed operators in Hilbert spaces

Arup Majumdar, P. Sam Johnson, Ram N. Mohapatra

In this paper, we introduce the generalized Cauchy dual $w (T) = T (T^{*} T)^{†}$ of a closed operator $T$ with the closed range between Hilbert spaces and present intriguing fi…

math.FA2024

Hyers-Ulam Stability of Unbounded Closable Operators in Hilbert Spaces

Arup Majumdar, P. Sam Johnson, Ram N. Mohapatra

In this paper, we discuss the Hyers-Ulam stability of closable (unbounded) operators with several interesting examples. We also present results pertaining to the Hyers-Ulam stabili…

math.FA2024

$A$ -approximate point spectrum of $A$ -bounded operators in semi-Hilbertian spaces

Arup Majumdar, P. Sam Johnson

This paper delves into several characterizations of $A$ -approximate point spectrum of A-bounded operators acting on a complex semi-Hilbertian space $H$ and also investigates proper…

math.FA2024

A formula of $A$ -spectral radius for $A^{\frac{1}{2}}$ -adjoint operators on semi-Hilbertian spaces

Arup Majumdar, P. Sam Johnson

In this paper, we prove the relation $\frac{r _{A} ( T ) + r _{A} ( T ^{⋄} ) + ∣ r _{A} ( T ^{⋄} ) - r _{A} ( T ) ∣}{2} = sup {∣ λ ∣ : λ \in σ_{A} (T)}$ , where $A$ is a positive semidefin…

On the generalized Cauchy dual of closed operators in Hilbert spaces

Hyers-Ulam Stability of Unbounded Closable Operators in Hilbert Spaces

A-approximate point spectrum of A-bounded operators in semi-Hilbertian spaces

A formula of A-spectral radius for A21​-adjoint operators on semi-Hilbertian spaces

$A$ -approximate point spectrum of $A$ -bounded operators in semi-Hilbertian spaces

A formula of $A$ -spectral radius for $A^{\frac{1}{2}}$ -adjoint operators on semi-Hilbertian spaces