On completely continuous linear transformations

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...

On Completely Continuous Hankel Matrices1

1. Main theorem. Let x = (xo, xi, • • • ) be a sequence of complex numbers and let | x \ he the norm | x | = (^Z | x„ |2)1/2 2:0. Let an asterisk denote complex conjugation. If \x\ < <» and |y| < oo, let [x, y] = [y, x] denote the sum of the series ^T,xnyn, that is, the "scalar" product of y by x*. For a given x with a finite norm |x|, let x(t) denote a function of class i2(0, 27r) having the F...

On Absolutely Continuous Transformations

On One-Sided Ideals of Rings of Linear Transformations