# On isomorphic classification of tensor products ${E}_{\infty}\left(a\right)\otimes \u0302{E}_{\infty}^{\text{'}}\left(b\right)$

Goncharov A.; Zahariuta V.; Terzioğlu Tosun

- 1996

## Access Full Book

top## Abstract

top## How to cite

topGoncharov A., Zahariuta V., and Terzioğlu Tosun. On isomorphic classification of tensor products $E_{∞}(a) ⊗̂ E^{\prime }_{∞}(b)$. 1996. <http://eudml.org/doc/275828>.

@book{GoncharovA1996,

abstract = {Abstract
New linear topological invariants are introduced and utilized to give an isomorphic classification of tensor products of the type $E_\{∞\}(a) ⊗̂ E^\{\prime \}_\{∞\}(b)$, where $E_\{∞\}(a)$ is a power series space of infinite type. These invariants are modifications of those suggested earlier by Zahariuta. In particular, some new results are obtained for spaces of infinitely differentiable functions with values in a locally convex space X. These spaces coincide, up to isomorphism, with spaces L(s’,X) of all continuous linear operators into X from the dual space of the space s of rapidly decreasing sequences. Most of the results given here with proofs were announced in [12].CONTENTS
0. Introduction...............................................5
1. Preliminaries.............................................6
2. Power series space-valued case..............8
3. Main results..............................................9
4. F- and DF-subspaces.............................11
5. Quasidiagonal isomorphism....................13
6. Sufficiency...............................................14
7. Linear Topological Invariants (LTI)..........16
8. Necessary conditions..............................20
9. Spaces $s ⊗̂ E^\{\prime \}_∞(b)$............................22
10. Spaces $s^\{\prime \} ⊗̂ E_\{∞\}(a)$.......................23
References.................................................261991 Mathematics Subject Classification: 46A04, 46A45, 46A11, 46A32.},

author = {Goncharov A., Zahariuta V., Terzioğlu Tosun},

keywords = {linear topological invariants; isomorphic classification of tensor products; power series space; dual space of the space ; rapidly decreasing sequences},

language = {eng},

title = {On isomorphic classification of tensor products $E_\{∞\}(a) ⊗̂ E^\{\prime \}_\{∞\}(b)$},

url = {http://eudml.org/doc/275828},

year = {1996},

}

TY - BOOK

AU - Goncharov A.

AU - Zahariuta V.

AU - Terzioğlu Tosun

TI - On isomorphic classification of tensor products $E_{∞}(a) ⊗̂ E^{\prime }_{∞}(b)$

PY - 1996

AB - Abstract
New linear topological invariants are introduced and utilized to give an isomorphic classification of tensor products of the type $E_{∞}(a) ⊗̂ E^{\prime }_{∞}(b)$, where $E_{∞}(a)$ is a power series space of infinite type. These invariants are modifications of those suggested earlier by Zahariuta. In particular, some new results are obtained for spaces of infinitely differentiable functions with values in a locally convex space X. These spaces coincide, up to isomorphism, with spaces L(s’,X) of all continuous linear operators into X from the dual space of the space s of rapidly decreasing sequences. Most of the results given here with proofs were announced in [12].CONTENTS
0. Introduction...............................................5
1. Preliminaries.............................................6
2. Power series space-valued case..............8
3. Main results..............................................9
4. F- and DF-subspaces.............................11
5. Quasidiagonal isomorphism....................13
6. Sufficiency...............................................14
7. Linear Topological Invariants (LTI)..........16
8. Necessary conditions..............................20
9. Spaces $s ⊗̂ E^{\prime }_∞(b)$............................22
10. Spaces $s^{\prime } ⊗̂ E_{∞}(a)$.......................23
References.................................................261991 Mathematics Subject Classification: 46A04, 46A45, 46A11, 46A32.

LA - eng

KW - linear topological invariants; isomorphic classification of tensor products; power series space; dual space of the space ; rapidly decreasing sequences

UR - http://eudml.org/doc/275828

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.