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# On completeness of the set of root vectors for unbounded operators

### Abstract

For a closed linear operator $A$ in a Banach space, the notion of a vector accessible in the resolvent sense at infinity is introduced. It is shown that the set of such vectors coincides with the space of exponential type entire vectors of this operator and the linear span of root vectors if, in addition, the resolvent of $A$ is meromorphic. In the latter case, the completeness criteria for the set of root vectors are given in terms of behavior of the resolvent at infinity.

### Article Information

 Title On completeness of the set of root vectors for unbounded operators Source Methods Funct. Anal. Topology, Vol. 12 (2006), no. 4, 353-362 MathSciNet MR2279872 Copyright The Author(s) 2006 (CC BY-SA)

### Authors Information

Myroslav L. Gorbachuk
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

Valentyna I. Gorbachuk
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Myroslav L. Gorbachuk and Valentyna I. Gorbachuk, On completeness of the set of root vectors for unbounded operators, Methods Funct. Anal. Topology 12 (2006), no. 4, 353-362.

### BibTex

@article {MFAT369,
AUTHOR = {Gorbachuk, Myroslav L. and Gorbachuk, Valentyna I.},
TITLE = {On completeness of the set of root vectors for unbounded operators},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {12},
YEAR = {2006},
NUMBER = {4},
PAGES = {353-362},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=369},
}