On three problems from the Scottish Book connected with orthogonal systems

• Autorzy: A. Plichko , A. Razenkov
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1996
• Tom: 70
• Numer: 2
• Strony: 227-234

Daty

wydano

1996

otrzymano

1994-05-05

poprawiono

1995-07-11

Twórcy

autor

A. Plichko

• Institute of Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova 3b, 290053 Lviv, Ukraine

autor

A. Razenkov

• Institute of Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, Naukova 3b, 290053 Lviv, Ukraine

Bibliografia

• [1] V. I. Gurariĭ, The existence of a non-hereditarily complete family in an arbitrary separable Banach space, Zap. Nauchn. Semin. LOMI 92 (1979), 274-277 (in Russian).
• [2] S. Kaczmarz, O zupełności układów ortogonalnych [On completeness of orthogonal systems], Archiwum Towarzystwa Naukowego we Lwowie, Dział III 8 (5) (1936), 431-436 (in Polish).
• [3] K. S. Kazarian, On some properties of uniformly bounded orthonormal systems, Dokl. Rassh. Zased. Semin. Inst. Prikl. Mat. im. I. N. Vekua (Tbilisi) 3 (1988), no2, 41-44 (in Russian).
• [4] K. S. Kazarian, On a problem of S. Banach from the Scottish Book, Proc. Amer. Math. Soc. 110 (1990), 881-887.
• [5] R. D. Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, 1981.
• [6] A. M. Olevskiĭ, On approximation with the preservation of spectrum, Dokl. Akad. Nauk SSSR 311 (1990), 32-36 (in Russian).
• [7] R. I. Ovsepian and A. Pełczyński, On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bounded orthonormal systems in $L^2$, Studia Math. 54 (1975), 149-159.
• [8] A. N. Plichko, Selection in a Banach space of subspaces with some special properties and some properties of quasicomplements, Funktsional. Anal. i Prilozhen. 15 (1) (1981), 82-83 (in Russian).
• [9] A. M. Plichko and M. M. Popov, Symmetric function spaces on atomless probability spaces, Dissertationes Math. 306 (1990).
• [10] W. H. Ruckle, On the classification of biorthogonal sequences, Canad. J. Math. 26 (1974), 721-733.
• [11] I. Singer, Bases in Banach Spaces, II, Springer, Berlin, 1981.