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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/o196811565382e 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 vectorvalued 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 vectorvalued 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 latticevalued spaces was widely used.
Keywords: Banach lattice, \(\mathbb{B}\)cyclic Banach space, isomorphic classification
Language: Russian
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For citation: Tasoev, B. B. Embeddings into \(\mathbb{B}\)Cyclic Banach Spaces // Vladikavkaz Math. J., 2022, vol. 24, no. 4, pp. 127132 (in Russian). DOI 10.46698/o196811565382e ← Contents of issue 
 

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