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On certain subsets of Bochner integrable function spaces.

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...

On class A operators

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.

On coerciveness in Besov spaces for abstract parabolic equations of higher order

Yoshitaka Yamamoto (1999)

Studia Mathematica

We are concerned with a relation between parabolicity and coerciveness in Besov spaces for a higher order linear evolution equation in a Banach space. As proved in a preceding work, a higher order linear evolution equation enjoys coerciveness in Besov spaces under a certain parabolicity condition adopted and studied by several authors. We show that for a higher order linear evolution equation coerciveness in Besov spaces forces the parabolicity of the equation. We thus conclude that parabolicity...

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