Linear operators form the cornerstone of analysis in Banach spaces, offering a framework in which one can rigorously study continuity, spectral properties and stability. Banach space theory, with its ...

“In mathematics, a Hilbert space is an inner product space that is complete with respect to the norm defined by the inner product. Hilbert spaces serve to clarify and generalize the concept of Fourier ...

Abstract: This study focuses on analyzing the convergence of the product of sequences and investigating the Cauchy sequences under specific conditions within neutrosophic normed linear spaces (NNLS).

ABSTRACT: For a ω-hyponormal operator T acting on a separable complex Hilbert space , we prove that: 1) the quasi-nilpotent part H0 (T－λI) is equal to ker(T－λI); 2) T has Bishop’s property β; 3) if σω ...

The main aim of this book is to provide an advanced textbook on functional analysis, focusing on the functional calculus of operators. Based on basic knowledge of functional analysis on metric spaces ...

Department of Mathematics, Duquesne University, Pittsburgh, USA. Theorem 2.1 also generalizes the result in [4] and provides a partial converse to Theorem 1 in [1, p. 372]. Our next main result in ...

In this paper, the reverse order law of Drazin inverse is investigated under some conditions in a Banach space. Moreover, the Drazin invertibility of sum for two bounded linear operators are also ...