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On some geometric properties of certain Köthe sequence spaces

Yunan Cui, Henryk Hudzik, Tao Zhang (1999)

Mathematica Bohemica

It is proved that if a Kothe sequence space X is monotone complete and has the weakly convergent sequence coefficient WCS ( X ) > 1 , then X is order continuous. It is shown that a weakly sequentially complete Kothe sequence space X is compactly locally uniformly rotund if and only if the norm in X is equi-absolutely continuous. The dual of the product space ( i = 1 X i ) Φ of a sequence of Banach spaces ( X i ) i = 1 , which is built by using an Orlicz function Φ satisfying the Δ 2 -condition, is computed isometrically (i.e. the exact...

On the diametral dimension of weighted spaces of analytic germs

Michael Langenbruch (2016)

Studia Mathematica

We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces S ¹ α and S α for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.

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