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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

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