On bases and the shift operator
J. Holub (1981)
Studia Mathematica
Çiğdem Atakut, Nurhayat İspir (2004)
Mathematica Slovaca
M.A. Fugarolas (1984)
Monatshefte für Mathematik
Eve Oja (2010)
Banach Center Publications
This survey features some recent developments concerning the bounded approximation property in Banach spaces. As a central theme, we discuss the weak bounded approximation property and the approximation property which is bounded for a Banach operator ideal. We also include an overview around the related long-standing open problem: Is the approximation property of a dual Banach space always metric?
A. L. Barrenechea, C. C. Peña (2009)
Publications de l'Institut Mathématique
Winfried Sickel (1989)
Czechoslovak Mathematical Journal
Harman, Aziz, Mamedov, Farman Imran (2010)
Journal of Inequalities and Applications [electronic only]
Krzysztof Nowak (1993)
Monatshefte für Mathematik
S.C. Arora (1974)
Publications de l'Institut Mathématique [Elektronische Ressource]
Noor, Muhammad Aslam (1996)
Journal of Applied Mathematics and Stochastic Analysis
Fernando Bombal (1991)
Extracta Mathematicae
One of the most important methods used in literature to introduce new properties in a Banach space E, consists in establishing some non trivial relationships between different classes of subsets of E. For instance, E is reflexive, or has finite dimension, if and only if every bounded subset is weakly relatively compact or norm relatively compact, respectively.On the other hand, Banach spaces of the type C(K) and Lp(μ) play a vital role in the general theory of Banach spaces. Their structure is so...
Sano, Takashi (2007)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
H. Millington (1974)
Mathematische Annalen
Sungeun Jung, Eungil Ko, Mee-Jung Lee (2010)
Studia Mathematica
We show that every class A operator has a scalar extension. In particular, such operators with rich spectra have nontrivial invariant subspaces. Also we give some spectral properties of the scalar extension of a class A operator. Finally, we show that every class A operator is nonhypertransitive.
Yang, Changsen, Zhao, Yuliang (2007)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Pushpa Juneja (1978)
Publications de l'Institut Mathématique
Karel Horák, Vladimír Müller (1993)
Czechoslovak Mathematical Journal
Konrad Schmüdgen (1986)
Manuscripta mathematica
Pavla Gvozdková (1970)
Commentationes Mathematicae Universitatis Carolinae
Wilhelmina Smajdor (2010)
Annales Polonici Mathematici
Let I ⊂ ℝ be an interval, Y be a normed linear space and Z be a Banach space. We investigate the Banach space Lip₂(I,Z) of all functions ψ: I → Z such that , where [r,s,t;ψ]:= ((s-r)ψ(t)+(t-s)ψ(r)-(t-r)ψ(s))/((t-r)(t-s)(s-r)). We show that ψ ∈ Lip₂(I,Z) if and only if ψ is differentiable and its derivative ψ’ is Lipschitzian. Suppose the composition operator N generated by h: I × Y → Z, (Nφ)(t):= h(t,φ(t)), maps the set (I,Y) of all affine functions φ: I → Y into Lip₂(I,Z). We prove that if N is...