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# About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator

### Abstract

In the paper, we describe a class of operators $A$ that have empty spectrum and satisfy the nilpotency property of the generated $C_0$-semigroup $U(t)=\exp\{-iAt\},\, t\geqslant 0$, and such that the operator$A^{-1}$ is similar to the integration operator on the corresponding space $L_2(0,a)$.

### Article Information

 Title About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 1, 60-66 MathSciNet MR2402153 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

G. V. Lukashenko
Poltava National Technical University, 24 Pervomaiskii prospect, Poltava, 36011, Ukraine

G. M. Gubreev
Poltava National Technical University, 24 Pervomaiskii prospect, Poltava, 36011, Ukraine

### Citation Example

G. V. Lukashenko and G. M. Gubreev, About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator, Methods Funct. Anal. Topology 14 (2008), no. 1, 60-66.

### BibTex

@article {MFAT444,
AUTHOR = {Lukashenko, G. V. and Gubreev, G. M.},
TITLE = {About nilpotent $C_0$-semigroups of operators in the Hilbert spaces and criteria for similarity to the integration operator},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {1},
PAGES = {60-66},
ISSN = {1029-3531},
MRNUMBER = {MR2402153},
URL = {http://mfat.imath.kiev.ua/article/?id=444},
}