On three problems from the Scottish Book connected with orthogonal systems

A. Plichko; A. Razenkov

Colloquium Mathematicae (1996)

  • Volume: 70, Issue: 2, page 227-234
  • ISSN: 0010-1354

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Plichko, A., and Razenkov, A.. "On three problems from the Scottish Book connected with orthogonal systems." Colloquium Mathematicae 70.2 (1996): 227-234. <http://eudml.org/doc/210408>.

@article{Plichko1996,
author = {Plichko, A., Razenkov, A.},
journal = {Colloquium Mathematicae},
keywords = {non-strong -basis; orthogonal system; conditional basis; -basis},
language = {eng},
number = {2},
pages = {227-234},
title = {On three problems from the Scottish Book connected with orthogonal systems},
url = {http://eudml.org/doc/210408},
volume = {70},
year = {1996},
}

TY - JOUR
AU - Plichko, A.
AU - Razenkov, A.
TI - On three problems from the Scottish Book connected with orthogonal systems
JO - Colloquium Mathematicae
PY - 1996
VL - 70
IS - 2
SP - 227
EP - 234
LA - eng
KW - non-strong -basis; orthogonal system; conditional basis; -basis
UR - http://eudml.org/doc/210408
ER -

References

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  1. [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. [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. [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. [4] K. S. Kazarian, On a problem of S. Banach from the Scottish Book, Proc. Amer. Math. Soc. 110 (1990), 881-887. Zbl0722.42014
  5. [5] R. D. Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, 1981. Zbl0485.01013
  6. [6] A. M. Olevskiĭ, On approximation with the preservation of spectrum, Dokl. Akad. Nauk SSSR 311 (1990), 32-36 (in Russian). 
  7. [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. Zbl0317.46019
  8. [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). Zbl0535.46008
  9. [9] A. M. Plichko and M. M. Popov, Symmetric function spaces on atomless probability spaces, Dissertationes Math. 306 (1990). 
  10. [10] W. H. Ruckle, On the classification of biorthogonal sequences, Canad. J. Math. 26 (1974), 721-733. Zbl0282.46013
  11. [11] I. Singer, Bases in Banach Spaces, II, Springer, Berlin, 1981. 

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