Some New Results on Strictly Singular Operators and Pre- Compact Operators

Characteristics and implications of simply singular operators

Abstract

A persistent straight administrator T E ⁇ F is viewed as absolutely particular if each limitless dimensional shut subspace of its area can't be invertible. In this notice, we address appropriate conditions and implications of the LB(E, F) = Ls(E, F) hypothesis, which implies that each continuous linear bounded operator described in E to F is strictly special. In the event that it maps an area of the source of E into a limited subset of F, a ceaseless direct administrator planning a neighborhood arched space (lcs) E into a lcs F is supposed to be limited If E or F is a uniform space, at that point any nonstop straight administrator is bound among E and F. A nonstop straight administrator T E on the same page F is viewed as simply solitary on the off chance that it isn't invertible on some vast shut subspace of E. Kato[13] added simply particular administrators to the class of Banach spaces as per the bother rule of Fredholm administrators.