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A note on one decomposition of Banach spaces


Abstract

For a scalar type spectral operator $A$ in complex Banach space $X$, the decomposition of $X$ into the direct sum \begin{equation*} X=\ker A\oplus \overline{R(A)}, \end{equation*} where $\ker A$ is the kernel of $A$ and $\overline{R(A)}$ is the closure of its range $R(A)$ is established.


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Article Information

TitleA note on one decomposition of Banach spaces
SourceMethods Funct. Anal. Topology, Vol. 12 (2006), no. 3, 254-257
MathSciNet MR2261579
CopyrightThe Author(s) 2006 (CC BY-SA)

Authors Information

M. V. Markin
Fresno, CA, USA 04.04.2006


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Citation Example

M. V. Markin, A note on one decomposition of Banach spaces, Methods Funct. Anal. Topology 12 (2006), no. 3, 254-257.


BibTex

@article {MFAT380,
    AUTHOR = {Markin, M. V.},
     TITLE = {A note on one decomposition of Banach spaces},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {12},
      YEAR = {2006},
    NUMBER = {3},
     PAGES = {254-257},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=380},
}


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