Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces

Details Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces

1993-10-11

arxiv.org/abs/math/9310216v1

Mathematics

Functional Analysis

Scientific paper

We study $M$-ideals of compact operators by means of the property~$(M)$ introduced in \cite{Kal-M}. Our main result states for a separable Banach space $X$ that the space of compact operators on $X$ is an $M$-ideal in the space of bounded operators if (and only if) $X$ does not contain a copy of $\ell_{1}$, has the metric compact approximation property, and has property~$(M)$. The investigation of special versions of property~$(M)$ leads to results on almost isometric structure of some classes of Banach spaces. For instance, we give a simple necessary and sufficient condition for a Banach space to embed almost isometrically into an $\ell_{p}$-sum of finite-dimensional spaces resp.\ into $c_{0}$, and for $2

Affiliated with

Also associated with

No associations

Rating

Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Property $(M)$, $M$-ideals, and almost isometric structure of Banach spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-267827