Norms on direct sums and tensor products

Authors:
P. Lancaster and H. K. Farahat

Journal:
Math. Comp. **26** (1972), 401-414

MSC:
Primary 46M05

DOI:
https://doi.org/10.1090/S0025-5718-1972-0305099-X

MathSciNet review:
0305099

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Abstract: We first consider the construction of a norm on a direct sum of normed linear spaces and call a norm absolute if it depends only on the norms of the component spaces. Several characterizations are given of absolute norms. Absolute norms are then used to construct norms on tensor products of normed linear spaces and on tensor products of operators on normed linear spaces.

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DOI:
https://doi.org/10.1090/S0025-5718-1972-0305099-X

Article copyright:
© Copyright 1972
American Mathematical Society