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Some consequences of the existence of an unbounded operator between Frechet Spaces.
Date
1984
Author
Yurdakul, Murat H
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Subject Keywords
Frechet spaces.
,
Locally convex spaces.
URI
https://hdl.handle.net/11511/11569
Collections
Graduate School of Natural and Applied Sciences, Thesis
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In this note, we obtain that all separable Frechet-Hilbert spaces have the property of smallness up to a complemented Banach subspace (SCBS). Djakov, Terzioglu, Yurdakul, and Zahariuta proved that a bounded perturbation of an automorphism on Frechet spaces with the SCBS property is stable up to a complemented Banach subspace. Considering Frechet-Hilbert spaces we show that the bounded perturbation of an automorphism on a separable Frechet-Hilbert space still takes place up to a complemented Hilbert subspace...
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This thesis takes its motivation from the theory of isomorphic classification of Cartesian products of locally convex spaces which was introduced by V. P. Zahariuta in 1973. In the case $X_1 times X_2 cong Y_1 times Y_2$ for locally convex spaces $X_i$ and $Y_i,i=1,2$; it is proved that if $X_1,Y_2$ and $Y_1,X_2$ are in compact relation in operator sense, it is possible to say that the respective factors of the Cartesian products are also isomorphic, up to their some finite dimensional subspaces. Zahariuta ...
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M. H. Yurdakul, “Some consequences of the existence of an unbounded operator between Frechet Spaces.,” Ph.D. - Doctoral Program, Middle East Technical University, 1984.