Topological Problems of H-Limits of Hausdorff Spectra of H-Spaces
by
Eugeny Smirnov
Pedagogical University, Yaroslavl, Russia

This note gives a wide generalisation of the direct and the converse spectra of objects of additive semi - abelian category J - the notion of Hausdorff spectrum similar to the \deltas - operation in the descriptive theory of sets ( for exsample, J = TLC ).

The construction of Hausdorff spectra \bold X = { X_s, \bold F, h_{s¹ s} } is achieved by successive standart expansion of small category of index \bold\Omega and uses the original topological methods. The direct and converse spectra of category J are particular cases of Hausdorff spectra. The action of functor of the countable Hausdorff spectra over the category of Banach spaces determines a local convex H - space class X which contains the category of Freshet spaces, De Wilde spaces:

X = \cup F in \bold F \cap s in F Xs          (s in \bold\Omega)

The strenghed variant of the closed graph theorem holds true for H - spaces. Theorem Countable separated regular H - limit of Hausdorff spectrum of H - space in category TLC is H - space.

References

[1]. Zabreiko P.P., Smirnov E.I. On the principles of uniform boundedness, Math. Notes , v.35 (1984), n.1, 287-297.

[2]. Smirnov E.I. Hausdorff Spectra in Functional Analysis. Monograph, Moscow , 1991.

[3]. Smirnov E.I. Hausdorff Spectra and the closed graph theorem. Pitman Research Notes in Math.Series , Proceedings Volum (1994), 37-50.

Date received: April 17, 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-11.