Norms on direct sums and tensor products
HTML articles powered by AMS MathViewer
- by P. Lancaster and H. K. Farahat PDF
- Math. Comp. 26 (1972), 401-414 Request permission
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.References
- F. L. Bauer, J. Stoer, and C. Witzgall, Absolute and monotonic norms, Numer. Math. 3 (1961), 257–264. MR 130104, DOI 10.1007/BF01386026
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- A. M. Ostrowski, On some metrical properties of operator matrices and matrices partitioned into blocks, J. Math. Anal. Appl. 2 (1961), 161–209. MR 130561, DOI 10.1016/0022-247X(61)90030-0
- Robert Schatten, A Theory of Cross-Spaces, Annals of Mathematics Studies, No. 26, Princeton University Press, Princeton, N. J., 1950. MR 0036935
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 401-414
- MSC: Primary 46M05
- DOI: https://doi.org/10.1090/S0025-5718-1972-0305099-X
- MathSciNet review: 0305099