Banach Journal of Mathematical Analysis

Isometric uniqueness of a complementably universal Banach space for Schauder decompositions

Joanna Garbulinska-Wegrzyn

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We present an isometric version of the complementably universal Banach space $\mathbb{P}$ with a Schauder decomposition. The space $\mathbb{P}$ is isomorphic to Pelczynski's space with a universal basis as well as to Kadec' complementably universal space with the bounded approximation property.

Article information

Banach J. Math. Anal., Volume 8, Number 1 (2014), 211-220.

First available in Project Euclid: 14 October 2013

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B04: Isometric theory of Banach spaces
Secondary: 46M40: Inductive and projective limits [See also 46A13] 46M40: Inductive and projective limits [See also 46A13] 46M15: Categories, functors {For $K$-theory, EXT, etc., see 19K33, 46L80, 46M18, 46M20}

complementably universal Banach space projection linear isometry


Garbulinska-Wegrzyn, Joanna. Isometric uniqueness of a complementably universal Banach space for Schauder decompositions. Banach J. Math. Anal. 8 (2014), no. 1, 211--220. doi:10.15352/bjma/1381782097.

Export citation


  • A. Avilés, F. Cabello Sánchez, J.M.F. Castillo, M. González and Y. Moreno, Banach spaces of universal disposition, J. Funct. Anal. 261 (2011), 2347–2361.
  • M. Droste and R. Göbel, A categorical theorem on universal objects and its application in abelian group theory and computer science, Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989), 49–74, Contemp. Math., 131, Part 3, Amer. Math. Soc., Providence, RI, 1992.
  • M. Fabian, P. Habala, P. Hájek, V. Montesinos and V. Zizler, Banach Space Theory. The Basis for Linear and Nonlinear Analysis, CMS Books in Mathematics. Springer, New York, 2011.
  • R. Fraïssé, Sur quelques classifications des systèmes de relations, Publ. Sci. Univ. Alger. Sér. A. 1 (1954), 35–182.
  • W.B. Johnson and A. Szankowski, Complementably universal Banach spaces, Studia Math. 58 (1976), 91–97.
  • M. I. Kadec, On complementably universal Banach spaces, Studia Math. 40 (1971), 85–89.
  • W. Kubiś, Fraïssé sequences: category-theoretic approch to universal homogeneus structures, preprint,
  • W. Kubiś and S. Solecki, A proof of uniqueness of the Gurarii space, to appear in Israel J. Math.,
  • A. Pełczyński, Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math. 40 (1971), 239–243.
  • A. Pełczyński, Universal bases, Studia Math. 32 (1969), 247–268.
  • A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209–228.
  • A. Pełczyński and P. Wojtaszczyk, Banach spaces with finite dimensional expansions of identity and universal bases of finite dimensional subspaces, Studia Math. 40 (1971), 91–108.