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Tensor products and the joint spectrum in Hilbert spaces

Authors: Zoia Ceauşescu and F.-H. Vasilescu
Journal: Proc. Amer. Math. Soc. 72 (1978), 505-508
MSC: Primary 47A10; Secondary 46M05
MathSciNet review: 509243
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Abstract: Given two complex Hilbert spaces X and Y and two commuting systems of linear continuous operators $ a = ({a_1}, \ldots ,{a_n})$ on X and $ b = ({b_1}, \ldots ,{b_m})$ on Y, the joint spectrum of the commuting system $ ({a_1} \otimes 1, \ldots ,{a_n} \otimes 1,1 \otimes {b_1}, \ldots ,1 \otimes {b_m})$ on $ X\bar \otimes Y$ is expressed by the Cartesian product of the joint spectrum of a with the joint spectrum of b.

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

  • [1] A. Brown and C. Pearcy, Spectra of tensor products of opeators, Proc. Amer. Math. Soc. 17 (1966), 162-166. MR 0188786 (32:6218)
  • [2] Z. Ceauşescu and F.-H. Vasilescu, Tensor products and Taylor's joint spectrum, Studia Math. (to appear).
  • [3] A. T. Dash and M. Schechter, Tensor products and joint spectra, Israel J. Math. 8 (1970), 191-193. MR 0261377 (41:5992)
  • [4] S. Mac Lane, Homology, Springer, New York, 1970. MR 1344215 (96d:18001)
  • [5] J. L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172-191. MR 0268706 (42:3603)
  • [6] F.-H. Vasilescu, A characterization of the joint spectrum in Hilbert spaces, Rev. Roumaine Math. Pures Appl. 22 (1977), 1003-1010. MR 0500211 (58:17890)

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Keywords: Tensor product, Hilbert space, joint spectrum
Article copyright: © Copyright 1978 American Mathematical Society

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