On approximate orthogonality and symmetry of operators in semi-Hilbertian structure
Abstract
The purpose of the article is to generalize the concept of approximate Birkhoff-James orthogonality, in the semi-Hilbertian structure. Given a positive operator A on a Hilbert space H, we define (ε,A)- approximate orthogonality and (ε,A)- approximate orthogonality in the sense of Chmielinski and establish a relation between them. We also characterize (ε,A)- approximate orthogonality in the sense of Chmielinski for A-bounded and A-bounded compact operators. We further generalize the concept of right symmetric and left symmetric operators on a Hilbert space. The utility of these notions are illustrated by extending some of the previous results obtained by various authors in the setting of Hilbert spaces.
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