Skip to main content
Journal cover image

Tensor products of closed operators on Banach spaces

Publication ,  Journal Article
Reed, M; Simon, B
Published in: Journal of Functional Analysis
January 1, 1973

Let A and B be closed operators on Banach spaces X and Y. Assume that A and B have nonempty resolvent sets and that the spectra of A and B are unbounded. Let α be a uniform cross norm on X ⊗ Y. Using the Gelfand theory and resolvent algebra techniques, a spectral mapping theorem is proven for a certain class of rational functions of A and B. The class of admissable rational functions (including polynomials) depends on the spectra of A and B. The theory is applied to the cases A ⊗ I + I ⊗ B and A ⊗ B where A and B are the generators of bounded holomorphic semigroups. © 1973.

Duke Scholars

Published In

Journal of Functional Analysis

DOI

EISSN

1096-0783

ISSN

0022-1236

Publication Date

January 1, 1973

Volume

13

Issue

2

Start / End Page

107 / 124

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Reed, M., & Simon, B. (1973). Tensor products of closed operators on Banach spaces. Journal of Functional Analysis, 13(2), 107–124. https://doi.org/10.1016/0022-1236(73)90038-4
Reed, M., and B. Simon. “Tensor products of closed operators on Banach spaces.” Journal of Functional Analysis 13, no. 2 (January 1, 1973): 107–24. https://doi.org/10.1016/0022-1236(73)90038-4.
Reed M, Simon B. Tensor products of closed operators on Banach spaces. Journal of Functional Analysis. 1973 Jan 1;13(2):107–24.
Reed, M., and B. Simon. “Tensor products of closed operators on Banach spaces.” Journal of Functional Analysis, vol. 13, no. 2, Jan. 1973, pp. 107–24. Scopus, doi:10.1016/0022-1236(73)90038-4.
Reed M, Simon B. Tensor products of closed operators on Banach spaces. Journal of Functional Analysis. 1973 Jan 1;13(2):107–124.
Journal cover image

Published In

Journal of Functional Analysis

DOI

EISSN

1096-0783

ISSN

0022-1236

Publication Date

January 1, 1973

Volume

13

Issue

2

Start / End Page

107 / 124

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics