9 papers
Some Generalized Numerical Ranges of Real-linear Operators on Hilbert Spaces
Arup Majumdar, Vladimir Muller
This paper introduces and systematically investigates several classes of numerical ranges associated with real-linear operators on Hilbert spaces, including the essential numerical…
Unbounded Antilinear Operators on Hilbert Spaces
Arup Majumdar
The paper introduces unbounded antilinear operators on Hilbert spaces and develops their fundamental theory. In particular, we establish a closed range theorem, a polar decompositi…
Spectral Properties of Off Diagonal Block Linear Relations via Moore Penrose Inverses in Hilbert Spaces
Arup Majumdar
In this paper, we characterize the essential spectra and the resolvent set of the off-diagonal block linear relation \[ \begin{bmatrix} 0 & A \\ B & 0 \end{bmatrix} \] in terms of…
Hyers-Ulam stability of closed linear relations in Hilbert spaces
Arup Majumdar
This paper introduces the concept of Hyers-Ulam stability for linear relations in normed linear spaces and presents several intriguing results that characterize the Hyers-Ulam stab…
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 of a closed operator with the closed range between Hilbert spaces and present intriguing fi…
Characterizations of closed EP operators on Hilbert spaces
Arup Majumdar, P. Sam Johnson
In this paper, we present intriguing findings that characterize both the closed (unbounded) and bounded EP operators on Hilbert spaces. Additionally, we demonstrate the result $γ(T…
The Moore-Penrose inverses of unbounded closable operators and the Cartesian product of closed operators in Hilbert spaces
Arup Majumdar, P. Sam Johnson
In this paper, we present some interesting results to characterize the Moore-Penrose inverses of unbounded closable operators and the Cartesian product of closed operators in Hilbe…
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…
A formula of -spectral radius for -adjoint operators on semi-Hilbertian spaces
Arup Majumdar, P. Sam Johnson
In this paper, we prove the relation , where is a positive semidefin…