Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Tensor product bases and tensor diagonals


Author: J. R. Holub
Journal: Trans. Amer. Math. Soc. 151 (1970), 563-579
MSC: Primary 46.10
DOI: https://doi.org/10.1090/S0002-9947-1970-0279564-2
MathSciNet review: 0279564
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let X and Y denote Banach spaces with bases $ ({x_i})$ and $ ({y_i})$, respectively, and let $ X{ \otimes _\varepsilon }Y$ and $ X{ \otimes _\pi }Y$ denote the completion in the $ \varepsilon $ and $ \pi $ crossnorms of the algebraic tensor product $ X \otimes Y$.

The purpose of this paper is to study the structure of the tensor product spaces $ X{ \otimes _\varepsilon }Y$ and $ X{ \otimes _\pi }Y$ through a consideration of the properties of the tensor product basis $ ({x_i} \otimes {y_j})$ for these spaces and the tensor diagonal $ ({x_i} \otimes {y_i})$ of such bases.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 46.10

Retrieve articles in all journals with MSC: 46.10


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0279564-2
Keywords: Tensor product, Schauder basis, tensor product basis, tensor diagonal
Article copyright: © Copyright 1970 American Mathematical Society