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Proceedings of the American Mathematical Society

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Tensor products and joint numerical range


Author: A. T. Dash
Journal: Proc. Amer. Math. Soc. 40 (1973), 521-526
MSC: Primary 47A10
MathSciNet review: 0336380
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Abstract: It is shown that the joint numerical range of the tensor product of several operators is the cartesian product of their numerical ranges.


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

  • [1] A. T. Dash, Joint spectra, joint spectral sets and joint numerical range, Ph.D. Thesis, University of Toronto, 1969.
  • [2] A. T. Dash, Joint spectra, Studia Math. 45 (1973), 225–237. MR 0336381
  • [3] J. Dixmier, Les algèbres d'opéprateurs dans l'espace Hilbertien, Gauthier-Villars, Paris, 1969.
  • [4] N. Dekker, Ph.D. Thesis, Amsterdam, 1969.
  • [5] A. T. Dash and M. Schechter, Tensor products and joint spectra, Israel J. Math. 8 (1970), 191–193. MR 0261377
  • [6] A. Guichardet, Tensor products of $ C\ast$ -algebras, Lecture Notes Series, nos. 12, 13, Aarhus Universitet, Mathematisk Institut, Denmark, 1969.
  • [7] Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
  • [8] François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0336380-9
Keywords: Algebra of operators, tensor products, convex sets, joint spectrum, joint numerical range, double commutant, commutative Banach algebra, universal property
Article copyright: © Copyright 1973 American Mathematical Society