Vol. 46, No. 2, 1973

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 331: 1  2
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
Uniform crossnorms

Barry Simon

Vol. 46 (1973), No. 2, 555–560
Abstract

A crossnorm on a pair of Banach spaces (X,Y ) is a norm, α, on the algebraic tensor product X Y obeying α(x y) = x∥∥yfor alI x X,y Y. When Schatten introduced crossnorms, he singled out two general classes of crossnorms: the dualizable crossnorms (called by him “crossnorms whose associates are crossnorms”) and the uniform crossnorms. These are crossnorms which induce in a natural way other crossnorms: in the dualizable case, a crossnorm, αd, on XY , and in the uniform case, a crossnorm, α, on (X) ⊙ℒ(Y ) where (X) is the algebra of bounded operators on X. Our main new result is a proof that if α is a uniform crossnorm, then α, the induced crossnorm on (X) ⊙ℒ(Y ) is dualizable.

Mathematical Subject Classification 2000
Primary: 46M05
Milestones
Published: 1 June 1973
Authors
Barry Simon
Department of Mathematics
California Institute of Technology
MC 253-37
Pasadena CA 91125
United States
http://www.math.caltech.edu/people/simon.html