Abstract
We study the properties of common spectral subspaces of the N generators of one-parameter (C0)-groups on different Banach spaces. The method of study is based on the functional calculus in the convolution algebra L1 (RN). We establish a theorem on the equality of the common spectra of the generators and their restrictions to common spectral subspaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
I. M. Gel'fand, “On one-parameter groups of operators in a normed space,”Dokl. Akad. Nauk SSSR,25, 711–716 (1939).
O. V. Lopushans'kii, “The operator calculus on ultrasmooth vectors,”Ukr. Mat. Zh.,44, No. 4, 502–513 (1992).
O. V. Lopushans'kii and V. A. Ryazhs'ka, “The spectral mapping theorem for holomorphic calculus of several variables of unbounded operators,”Mat. Stud.,8, No. 1, 97–110 (1997).
Yu. I. Lyubich and V. I. Matsaev, “On operators with separable spectrum,”Mat. Sb,56 (98), No. 4, 433–468 (1962).
S. M. Nikol'skii,Approximation of Functions of Several Variables and Imbedding Theorems, Springer, New York (1975).
Ya. V. Radyno, “Vectors of exponential type in operational calculus and differential equations,”Differents. Uravn.,44, No. 4, 502–513 (1985).
H. Schaefer,Topological Vector Spaces, Macmillan, New York (1966).
A. Grothendieck, “Produits tensoriels topologiques et espaces nucléaires,”Mem. Amer. Math. Soc.,16, No. 2, 1–140 (1955).
Additional information
Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 40–47.
Rights and permissions
About this article
Cite this article
Ryazhs'ka, V.A., Lopushans'kii, O.V. Spectral properties of generators of theC 0-groups over tensor products of Banach spaces. J Math Sci 96, 2973–2979 (1999). https://doi.org/10.1007/BF02169690
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02169690