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.

Full Text

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},
}