Complemented subspaces of sums and products of banach spaces

1988 ◽  
Vol 153 (1) ◽  
pp. 175-190 ◽  
Author(s):  
G. Metafune ◽  
V. B. Moscatelli
Keyword(s):  
Banach Spaces ◽  
Complemented Subspaces

scholarly journals On complemented subspaces of sums and products of Banach spaces

1996 ◽  
Vol 124 (7) ◽  
pp. 2005-2012
Author(s):  
M. I. Ostrovskii
Keyword(s):  
Banach Spaces ◽  
Complemented Subspaces

Some classes of Banach spaces and complemented subspaces of operators

2019 ◽  
Vol 4 (2) ◽  
pp. 369-387 ◽  
Author(s):  
Ioana Ghenciu
Keyword(s):  
Banach Spaces ◽  
Complemented Subspaces

Closed Complemented Subspaces of Banach Spaces and Existence of Bounded Quasi-linear Generalized Inverses

2017 ◽  
Vol 38 (11) ◽  
pp. 1490-1506
Author(s):  
Liu Guanqi ◽  
Henryk Hudzik ◽  
Wang Yuwen
Keyword(s):  
Banach Spaces ◽  
Generalized Inverses ◽  
Complemented Subspaces

Banach Spaces

2021 ◽  
pp. 245-289
Author(s):  
Adel N. Boules
Keyword(s):  
Banach Spaces ◽  
Uniform Boundedness ◽  
Linear Transformations ◽  
Closed Graph Theorem ◽  
Complemented Subspaces ◽  
Good Account ◽  
Banach Theorem ◽  
Schauder Bases ◽  
Uniform Boundedness Principle ◽  
Adjoint Operators

The first four sections of this chapter form its core and include classical topics such as bounded linear transformations, the open mapping theorem, the closed graph theorem, the uniform boundedness principle, and the Hahn-Banach theorem. The chapter includes a good number of applications of the four fundamental theorems of functional analysis. Sections 6.5 and 6.6 provide a good account of the properties of the spectrum and adjoint operators on Banach spaces. They may be largely bypassed, since the treatment of the corresponding topics for operators on Hilbert spaces in chapter 7 is self-contained. The section on weak topologies is more advanced and may be omitted if a brief introduction is the goal. The chapter is enriched by such topics as the best polynomial approximation, the Hilbert cube, Gelfand’s theorem, Schauder bases, complemented subspaces, and the Banach-Alaoglu theorem.

scholarly journals Complemented subspaces ofp-adic second dual Banach spaces

1995 ◽  
Vol 18 (3) ◽  
pp. 437-442
Author(s):  
Takemitsu Kiyosawa
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Complemented Subspaces ◽  
Complete Field ◽  
Second Dual

LetKbe a non-archimedean non-trivially valued complete field. In this paper we study Banach spaces overK. Some of main results are as follows: (1) The Banach spaceBC((l∞)1)has an orthocomplemented subspace linearly homeomorphic toc0. (2) The Banach spaceBC((c0)1)has an orthocomplemented subspace linearly homeomorphic tol∞.

Complemented Subspaces of Products of Banach Spaces

1989 ◽  
Vol 316 (1) ◽  
pp. 215 ◽  
Author(s):  
Pawel Domanski ◽  
Augustyn Ortynski
Keyword(s):  
Banach Spaces ◽  
Complemented Subspaces

scholarly journals On pseudo-complemented subspaces of Banach spaces

1973 ◽  
Vol 13 (3) ◽  
pp. 223-232 ◽  
Author(s):  
Ivan Singer
Keyword(s):  
Banach Spaces ◽  
Complemented Subspaces

COMPLEMENTATION AND EMBEDDINGS OF c0(I) IN BANACH SPACES

2002 ◽  
Vol 85 (3) ◽  
pp. 742-768 ◽  
Author(s):  
SPIROS A. ARGYROS ◽  
JESÚS F. CASTILLO ◽  
ANTONIO S. GRANERO ◽  
MAR JIMÉNEZ ◽  
JOSÉ P. MORENO
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Compact Subset ◽  
Continuum Hypothesis ◽  
Finite Partition ◽  
Weakly Compact ◽  
Complemented Subspaces ◽  
Generalized Continuum ◽  
Compactly Generated

We investigate in this paper the complementation of copies of $c_0(I)$ in some classes of Banach spaces (in the class of weakly compactly generated (WCG) Banach spaces, in the larger class $\mathcal{V}$ of Banach spaces which are subspaces of some $C(K)$ space with $K$ a Valdivia compact, and in the Banach spaces $C([1, \alpha ])$, where $\alpha$ is an ordinal) and the embedding of $c_0(I)$ in the elements of the class $\mathcal{C}$ of complemented subspaces of $C(K)$ spaces. Two of our results are as follows:(i) in a Banach space $X \in \mathcal{V}$ every copy of $c_0(I)$ with $\# I < \aleph _{\omega}$ is complemented;(ii) if $\alpha _0 = \aleph _0$, $\alpha _{n+1} = 2^{\alpha _n}$, $n \geq 0$, and $\alpha = \sup \{\alpha _n : n \geq 0\}$ there exists a WCG Banach space with an uncomplemented copy of $c_0(\alpha )$.So, under the generalized continuum hypothesis (GCH), $\aleph _{\omega}$ is the greatest cardinal $\tau$ such that every copy of $c_0(I)$ with $\# I < \tau$ is complemented in the class $\mathcal{V}$. If $T : c_0(I) \to C([1,\alpha ])$ is an isomorphism into its image, we prove that:(i) $c_0(I)$ is complemented, whenever $\| T \| ,\| T^{-1} \| < (3/2)^{\frac 12}$;(ii) there is a finite partition $\{I_1, \dots , I_k\}$ of $I$ such that each copy $T(c_0(I_k))$ is complemented.Concerning the class $\mathcal{C}$, we prove that an already known property of $C(K)$ spaces is still true for this class, namely, if $X \in \mathcal{C}$, the following are equivalent:(i) there is a weakly compact subset $W \subset X$ with ${\rm Dens}(W) = \tau$;(ii) $c_0(\tau )$ is isomorphically embedded into $X$.This yields a new characterization of a class of injective Banach spaces.2000 Mathematical Subject Classification: 46B20, 46B26.

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