OBSERVATIONS ABOUT THE PROJECTIVE TENSOR PRODUCT OF BANACH SPACES, I—

Abstract

A sequential description of the projective tensor product lp⊗X, is given. This description allows us to show the inclusion lp⊗X, into lp⊗X, is a semi-embedding. As a consequence, if X has the Radon-Nikodym property so does lp⊗X, A discussion of difficulties with L^p(0, 1) ⊗X, follows.

Mathematics Subject Classification (2000):

• 46A
• 46B
• 46E
• 47B

Key words:

• tensor product
• projective norm
• greatest crossnorm
• semi-embedding
• Radon-Nikodym property
• absolutely p-summable sequence
• strongly p-summable sequence