COMPLETELY CONTINUOUS SUBSPACES OF OPERATOR IDEALS

Completely Continuous Banach Algebras

For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a suffici...

Completely continuous Banach algebras

 For a Banach algebra $fA$, we introduce ~$c.c(fA)$, the set of all $phiin fA^*$ such that $theta_phi:fAto  fA^*$ is a completely continuous operator, where $theta_phi$ is defined by $theta_phi(a)=acdotphi$~~ for all $ain fA$. We call $fA$, a completely continuous Banach algebra if $c.c(fA)=fA^*$. We give some examples of completely continuous Banach algebras and a sufficient condition for an o...

Subspaces of Maximal Operator Spaces

A Banach space E can be embedded into B(H) in a variety of ways. The embeddings giving rise to the minimal and maximal possible operator space norms (introduced in [1], [3] and [4] and further investigated in [21] and [22]) are especially interesting to us. Let A be the set of all functionals on E of norm not exceeding 1 and let B be the set of all linear maps T : E → Mn such that ||T || ≤ 1 (h...

Generic local distinguishability and completely entangled subspaces

Commutator structure of operator ideals

Commutator structure of operator ideals Ken Dykema, ,1 Tadeusz Figiel, Gary Weiss, and Mariusz Wodzicki Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA b Instytut Matematyczny Polskiej Akademii Nauk, 81-825 Sopot, Poland Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA Department of Mathematics, University of Cali...