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Perfect sets of finite class without the extension property

A. Goncharov — 1997

Studia Mathematica

We prove that generalized Cantor sets of class α, α ≠ 2 have the extension property iff α < 2. Thus belonging of a compact set K to some finite class α cannot be a characterization for the existence of an extension operator. The result has some interconnection with potential theory.

Extension via interpolation

A. Goncharov — 2005

Banach Center Publications

We suggest a modification of the Pawłucki and Pleśniak method to construct a continuous linear extension operator by means of interpolation polynomials. As an illustration we present explicitly the extension operator for the space of Whitney functions given on the Cantor ternary set.

On isomorphic classification of tensor products E ( a ) ̂ E ' ( b )

Abstract New linear topological invariants are introduced and utilized to give an isomorphic classification of tensor products of the type E ( a ) ̂ E ' ( 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...

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