On Tensor Product of H-Spaces
by
G.E. Kozlov
Pedagogical University, Yaroslavl, Russia

A.Grothendieck's problem about the extention of classes of the locally convex spaces LCS , possesing the closed graph theorem and the broad properties of permanense, found the positive solution in the works of L.Schwartz, W.Slowikowsky, D.A.Raikov, M.De Wilde, P.P.Zabreiko, E.I.Smirnov and many others. The class of H - spaces of E.I.Smirnov is most broad from the similar classes. A LCS ( Y, \gamma) will be an H - space, if

Y = È F in \Omega  Ç t in F   Yt,

where Y_t (t in A) are seminormal spaces, A is not more than countable set of element t, Y_t subset Y , \Omega is some family of subsets from A and also every metric vector group Y_(F) (F in \Omega) is complete and continuously embedded in ( Y, \gamma) . A tensor product of H - spaces is the main aim of this note. Theorem Let ( X, \delta) and ( Y, \gamma) be sequential complete H - spaces and let X'_\tau be a sequential complete LSC . Then X [^(\otimes_\omega)]Y is H - spase. X'_\tau is a dual space of X with topology of Mackey. The sign [^(\otimes_\omega)] means a sequential completion of weak tensor product.

Reference

[1] Smirnov E.I. Hausdorff spectra in functional analysis. Monograph.- Moskow, 1991.P.166

[2] Kozlov G.E. Suslin's limit of the topology of A - modules and the tensor product of H -spaces. Yaroslavl, State Pedagogical University, 1993.P.21

Date received: May 20, 1997

Copyright © 1997 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caao-08.