Almost square and octahedral norms in tensor products of Banach spaces
Journal article, Peer reviewed
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Original versionRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2017, 111 (3), 841-853. 10.1007/s13398-016-0324-0
The aim of this note is to study some geometrical properties like diameter two properties, octahedrality and almost squareness in the setting of (symmetric) tensor product spaces. In particular, we show that the injective tensor product of two octahedral Banach spaces is always octahedral, the injective tensor product of an almost square Banach space with any Banach space is almost square, and the injective symmetric tensor product of an octahedral Banach space is octahedral.