Skip to main content
SpringerLink
Log in

On Markuševič decompositions of Banach spaces

О РАжлОжЕНИьх БАНАхО Вых пРОстРАНстВ пО МА РкУшЕВИЧУ

  • Published:
Analysis Mathematica Aims and scope Submit manuscript

Abstract

пРОВЕДЕНО сИстЕМАтИ ЧЕскОЕ ИсслЕДОВАНИЕ РАжлИЧНых тИпОВ РАжлОжЕНИИ, А ИМ ЕННО, пО МАРкУшЕВИЧУ, ОБОБЩЕН Ных И РАжлОжЕНИИ пО шА УДЕРУ. УкАжАНы пРИМЕРы, ИллУ стРИРУУЩИЕ ВжАИМООтНОшЕНИь ЁтИ х тИпОВ РАжлОжЕНИИ. Ос НОВНАь цЕль ДАННОИ РАБОты — ИжУЧЕ НИЕ РАжлОжЕНИИ пО МАРкУшЕВИЧУ (M-РАжл ОжЕНИИ). ОтМЕЧАЕтсь, Чт О пОслЕДОВАтЕльНОсть пРОЕкцИИ, сВьжАННАь с ОБОБЩЕНН ыМ РАжлОжЕНИЕМ, ьВльЕ тсь ЕДИНстВЕННОИ тОгДА И тОлькО тОгДА, кОгДА ЁтОM-РАжлОжЕНИЕ. пОлУ ЧЕНА хАРАктЕРИжАцИьM-РАжлОжЕНИИ В тЕРМИН Ах Их пОДпОслЕДОВАтЕ льНОстЕИ. пОлУЧЕНА тАкжЕ хАРАк тЕРИжАцИь пО шАУДЕРУ В тЕРМИНАхM-РАжлОжЕНИИ. НАкОНЕц, пОлУЧЕНы ОтНОшЕНИь Д ВОИстВЕННОстИ МЕжДУM-РАжлОжЕНИьМИ НЕкОтО РОгО пРОстРАНстВА И НЕкОтОРыМИ РАжлОжЕ НИьМИ сОпРьжЕННОгО п РОстРАНстВА.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. K. Ahmad andS. M. Maskey, Characterization of Schauder decomposition in Banach spaces,Acta Math. Hungar.,41 (1983), 283–290.

    Article  MATH  MathSciNet  Google Scholar 

  2. M. G. Arsove andR. E. Edwards, Generalized bases in topological linear spaces,Studia Math.,19 (1960), 95–113.

    MATH  MathSciNet  Google Scholar 

  3. D. Amir andJ. Lindenstrauss, The structure of weakly compact sets in Banach spaces,Ann. Math.,88 (1968), 35–46.

    Article  MathSciNet  Google Scholar 

  4. G. F. Bachelis andH. P. Rosenthal, On unconditionally converging series and biorthogonal systems in a Banach space,Pacific J. Math.,37 (1971), 1–5.

    MathSciNet  Google Scholar 

  5. W. H. Courage andW. J. Davis, A characterization ofM-basis,Math. Annalen,197 (1972), 1–4.

    Article  MATH  MathSciNet  Google Scholar 

  6. W. J. Davis, Schauder decompositions in Banach spaces,Bull. Amer. Math. Soc.,74 (1968), 1083–1085.

    Article  MATH  MathSciNet  Google Scholar 

  7. D. W. Dean, Schauder decompositions in (m),Proc. Amer. Math. Soc.,18 (1967), 619–623.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. K. Fage, Idempotent operators and their rectification,Dokl. Akad. Nauk SSSR,73 (1950), 895–897 (Russian).

    MATH  MathSciNet  Google Scholar 

  9. M. K. Fage, The rectification of bases in a Hilbert space,Dokl. Akad. Nauk SSSR,74 (1950), 1053–1056 (Russian).

    MATH  MathSciNet  Google Scholar 

  10. M. M. Grinblium, On the representation of a space of type B as a direct sum of subspaces,Dokl. Akad. Nauk SSSR,70 (1950), 749–752 (Russian).

    Google Scholar 

  11. P. K. Jain andK. Ahmad, Best approximation in Banach spaces with unconditional Schauder decomposition,Acta Sci. Math.,42 (1980), 275–279.

    MATH  MathSciNet  Google Scholar 

  12. P. K. Jain andK. Ahmad, Certain characterizations of Schauder decompositions in Banach space,Analele Mat.,19 (1981), 61–66.

    MathSciNet  Google Scholar 

  13. P. K. Jain andK. Ahmad, Best approximation in Banach spaces with Schauder decomposition,Tamkang J. Math.,12 (1981), 59–66.

    MATH  MathSciNet  Google Scholar 

  14. P. K. Jain andK. Ahmad, Unconditional Schauder decompositions and best approximation in Banach spaces,Indian J. Pure Appl. Math.,12 (1981), 1456–1467.

    MATH  MathSciNet  Google Scholar 

  15. P. K. Jain, K. Ahmad andS. M. Maskey, A note on boundedly complete decomposition of a Banach space,Acta Sci. Math.,44 (1982), 365–369.

    MATH  MathSciNet  Google Scholar 

  16. P. K. Jain, K. Ahmad andS. M. Maskey, Domination of sequence of subspaces in Banach spaces,Analele Mat.,24 (1986), 34–42.

    MATH  MathSciNet  Google Scholar 

  17. P. K. Jain, K. Ahmad andS. M. Maskey, Domination and equivalence of sequences of subspaces in dual spaces,Czechoslovak Math. J.,36 (111) (1986), 351–357.

    MathSciNet  Google Scholar 

  18. P. K. Jain andK. Ahmad, Schauder decomposition and best approximation in Banach spaces,Portugaliae Math.,44 (1987), 25–39.

    MATH  MathSciNet  Google Scholar 

  19. A. Markouchevitch, Sur les bases (au sens large) dans les espaces linéaires,Dokl. Akad. Nauk SSSR,41 (1943), 227–229 (Russian).

    MathSciNet  Google Scholar 

  20. C. W.McArthur, Infinite direct sums in metric linear spaces (unpublished).

  21. J. R. Retherford,w *-bases andw *-bases in Banach space,Studia Math.,25 (1964), 65–71.

    MATH  MathSciNet  Google Scholar 

  22. J. R. Retherford, Some remarks on Schauder bases of subspaces,Rev. Roumaine Math. Pures et Appl.,11 (1966), 787–792.

    MATH  MathSciNet  Google Scholar 

  23. J. R. Retherford, Some remarks on Schauder bases of subspaces. II,Rev. Roumaine Math. Pures et Appl.,13 (1968), 521–528.

    MATH  MathSciNet  Google Scholar 

  24. W. H. Ruckle, The infinite sum of closed subspaces of anF-space,Duke Math. J.,31 (1964), 543–554.

    Article  MATH  MathSciNet  Google Scholar 

  25. B. L. Sanders, On the existence of Schauder decompositions in Banach spaces,Proc. Amer. Math. Soc.,16 (1965), 987–990.

    Article  MATH  MathSciNet  Google Scholar 

  26. I. Singer, Bases in Banach spaces. II, Springer (Berlin, 1981).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Delhi, 110007, Delhi, India

    P. K. Jain & D. P. Sinha

Authors
  1. P. K. Jain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. P. Sinha
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research of the author was supported by the CSIR (India).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jain, P.K., Sinha, D.P. On Markuševič decompositions of Banach spaces. Analysis Mathematica 16, 265–275 (1990). https://doi.org/10.1007/BF02630360

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02630360

Keywords

Search

Navigation