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# Generalized selfadjoinness of differentiation operator on weight Hilbert spases

### Abstract

We consider examples of operators that act in some Hilbert rigging from positive Hilbert space into the negative one. For the first derivative operator we investigate a generalized'' selfadjointness in the sense of weight Hilbert riggings of the spaces $L^2([0,1])$ and $L^2(\mathbb{R})$. We will show that an example of the operator $i \frac{d}{dt}$ in some rigging scales, which is selfadjoint in usual case and not generalized selfadjoint, can not be constructed.

### Article Information

 Title Generalized selfadjoinness of differentiation operator on weight Hilbert spases Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 333-337 MathSciNet MR2374835 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

Ivan Ya. Ivasiuk
Department of Mathematical Analysis, National Taras Shevchenko University of Kyiv, Kyiv, Ukraine

### Citation Example

Ivan Ya. Ivasiuk, Generalized selfadjoinness of differentiation operator on weight Hilbert spases, Methods Funct. Anal. Topology 13 (2007), no. 4, 333-337.

### BibTex

@article {MFAT429,
AUTHOR = {Ivasiuk, Ivan Ya.},
TITLE = {Generalized selfadjoinness of differentiation operator on weight Hilbert spases},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {4},
PAGES = {333-337},
ISSN = {1029-3531},
MRNUMBER = {MR2374835},
URL = {http://mfat.imath.kiev.ua/article/?id=429},
}