On norming Markushevich bases

Ostrovskii M.I

A subclass of Markushevich bases in separable Banach spaces such that there exists a way to reconstruct vectors from their generalized Fourier series is introduced. It is proved that this subclass coincides with the class of norming Markushevich bases.

1. V.P.Fonf Operator bases and generalized summation bases // Dopovidi AN Ukrainy – 1986 N. 11 p. 16–18 Russian, Ukrainian

2. M.I.Kadets Non-linear operator bases in a Banach space // Teor. Funktsii, Funktsional. Anal. i Prilozhen. V. 2 – 1966 p. 128–130 Russian

3. A.I. Markushevich On a basis (in wide sense) for linear spaces // Dokl. Akad. Nauk SSSR V. 41 – 1943 p. 241–243 Russian

4. I.Singer Bases in Banach Spaces, v. II , Springer-Verlag ,addr Berlin Heidelberg New York – 1981. - 880 p

5. V.A.Vinokurov, Yu.I.Petunin and A.N.Plichko Measurability and regularizability of mappings that are inverses of continuous linear operators // Mat. Zametki V. 26 – 1979 N. 4 p. 583–591 Russian English transl. in // Math. Notes V. 26– 1979 p. 781–785

	On norming Markushevich bases
Author	Ostrovskii M.I mostrovskii@ilt.kharkov.ua
Abstract	A subclass of Markushevich bases in separable Banach spaces such that there exists a way to reconstruct vectors from their generalized Fourier series is introduced. It is proved that this subclass coincides with the class of norming Markushevich bases.
Keywords	Markushevich bases, reconstructing basis, Banach spaces, Fourier series, biorthogonal sequence
DOI	doi:10.30970/ms.5.1.39-42
Reference	1. V.P.Fonf Operator bases and generalized summation bases // Dopovidi AN Ukrainy – 1986 N. 11 p. 16–18 Russian, Ukrainian 2. M.I.Kadets Non-linear operator bases in a Banach space // Teor. Funktsii, Funktsional. Anal. i Prilozhen. V. 2 – 1966 p. 128–130 Russian 3. A.I. Markushevich On a basis (in wide sense) for linear spaces // Dokl. Akad. Nauk SSSR V. 41 – 1943 p. 241–243 Russian 4. I.Singer Bases in Banach Spaces, v. II , Springer-Verlag ,addr Berlin Heidelberg New York – 1981. - 880 p 5. V.A.Vinokurov, Yu.I.Petunin and A.N.Plichko Measurability and regularizability of mappings that are inverses of continuous linear operators // Mat. Zametki V. 26 – 1979 N. 4 p. 583–591 Russian English transl. in // Math. Notes V. 26– 1979 p. 781–785
Pages	39-42
Volume	5
Issue	1
Year	1995
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html