Finite-dimensional Schauder decompositions in certain Frechet spaces

Schauder decompositions in locally convex spaces

Unconditional Bases and Unconditional Finite-dimensional Decompositions in Banach Spaces

Let X he a Banach space with an unconditional finite-dimensional Schauder decomposition (En). We consider the general problem of characterizing conditions under which one can construct an unconditional basis for X by forming an unconditional basis for each En. For example, we show that if sup,, dim En < c~ and X has Gordon-Lewis local unconditional s t ructure then X has an unconditional basis ...

Extending Certain Transformation Group Actions in Separable, Infinite-dimensional Frechet Spaces and the Hilbert Cube

A theorem of V. L. Klee, Jr. [9] asserts that any homeomorphism between two compact sets in a separable, infinite-dimensional Hilbert space can be extended to a homeomorphism of the entire space onto itself. Since it has recently been shown ( [ l ] , [5] and [6]) that all separable, infinite-dimensional Frechet spaces are homeomorphic (a Frechet space being a metrizable, complete, locally conve...

Schauder Decompositions and Completeness

00 It x = S QnIf» m addition, the projections Pn = £ Q,are equicontinuous, then n = 1 « = 1 (£n)^°=1 is said to be an equi-Schauder decomposition of E. It is obvious that a Schauder basis is equivalent to a Schauder decomposition in which each subspace is one-dimensional, and that it is equi-Schauder if and only if the corresponding decomposition is equi-Schauder. For more information on Schaud...

Geometric Decompositions of 4-dimensional Bundle Spaces

We consider geometric decompositions of aspherical 4manifolds which fibre over 2-orbifolds. We show first that no such manifold admits infinitely many fibrations over hyperbolic base orbifolds. If E is Seifert fibred over a hyperbolic surface B and either B has at most one cone point of order 2 or the monodromy has image in SL(2,Z) then E it has a decomposition induced from a decomposition of B...