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DOI: 10.46698/o1968-1156-5382-e

Embeddings into \(\mathbb{B}\)-Cyclic Banach Spaces

Tasoev, B. B.
Vladikavkaz Mathematical Journal 2022. Vol. 24. Issue 4.
Abstract:
For a complete Boolean algebra \(\mathbb{B}\) and nonzero \(\pi\in \mathbb{B}\), the notion of an \(\mathbb{B}_{\pi}\)-embedding of Banach spaces into \(\mathbb{B}\)-cyclic Banach spaces is introduced. The notion of a lattice \(\mathbb{B}_{\pi}\)-embedding of Banach lattices into \(\mathbb{B}\)-cyclic Banach lattices is also introduced. A criterion for the \(\mathbb{B}_{\pi}\)-embedding of a space of continuous vector-valued functions with values in an arbitrary Banach space into a \(\mathbb{B}\)-cyclic Banach space is established, as well as a criterion for the lattice \(\mathbb{B}_{\pi}\)-embedding of a space of continuous vector-valued functions with values in an arbitrary Banach lattice into a \(\mathbb{B}\)-cyclic Banach lattice. The obtained results allow us to outline an approach for isometric and isomorphic classification of \(\mathbb{B}\)-cyclic Banach spaces. In the course of establishing the results, the tool of lattice-valued spaces was widely used.
Keywords: Banach lattice, \(\mathbb{B}\)-cyclic Banach space, isomorphic classification
Language: Russian Download the full text  
For citation: Tasoev, B. B. Embeddings into \(\mathbb{B}\)-Cyclic Banach Spaces // Vladikavkaz Math. J., 2022, vol. 24, no. 4, pp. 127-132 (in Russian). DOI 10.46698/o1968-1156-5382-e
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