Tensor products and the joint spectrum in Hilbert spaces

Ceauşescu, Zoia; Vasilescu, F.-H.

doi:10.1090/S0002-9939-1978-0509243-8

Tensor products and the joint spectrum in Hilbert spaces
HTML articles powered by AMS MathViewer

by Zoia Ceauşescu and F.-H. Vasilescu PDF

Proc. Amer. Math. Soc. 72 (1978), 505-508 Request permission

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

Arlen Brown and Carl Pearcy, Spectra of tensor products of operators, Proc. Amer. Math. Soc. 17 (1966), 162–166. MR 188786, DOI 10.1090/S0002-9939-1966-0188786-5

Tensor products and Taylor’s joint spectrum

A. T. Dash and M. Schechter, Tensor products and joint spectra, Israel J. Math. 8 (1970), 191–193. MR 261377, DOI 10.1007/BF02771314
Saunders Mac Lane, Homology, Classics in Mathematics, Springer-Verlag, Berlin, 1995. Reprint of the 1975 edition. MR 1344215
Joseph L. Taylor, A joint spectrum for several commuting operators, J. Functional Analysis 6 (1970), 172–191. MR 0268706, DOI 10.1016/0022-1236(70)90055-8
F.-H. Vasilescu, A characterization of the joint spectrum in Hilbert spaces, Rev. Roumaine Math. Pures Appl. 22 (1977), no. 7, 1003–1009. MR 500211