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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.

On the representation of uncountable symmetric basic sets and its applications

Francisco Hernandez, Stanimir Troyanski (1993)

Studia Mathematica

It is shown that every uncountable symmetric basic set in an F-space with a symmetric basis is equivalent to a basic set generated by one vector. We apply this result to investigate the structure of uncountable symmetric basic sets in Orlicz and Lorentz spaces.

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