we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

We prove some structure results for isometries between noncommutative L spaces associated to von Neumann algebras. We find that an isometry T : L(M1) → L(M2) (1 ≤ p < ∞, p 6= 2) can be canonically expressed in a certain simple form whenever M1 has variants of Watanabe’s extension property [W2]. Conversely, this form always defines an isometry provided that M1 is “approximately semifinite” (defi...

Let λ > 0 , Zp,q denote R2 endowed with the norm |x|p,q = (‖x‖p +λ‖x‖q) 1 2 . Recently, James constant J(Zp,q) and von Neumann-Jordan constant CNJ(Zp,q) have been investigated under the two cases of a space 2 p q ∞ and 1 p q 2 . In this note, we show an inequality on these two constants under the case of 1 p 2 q ∞ . As an application, we give a sufficient condition for the space Zp,q with unifo...