On stability of distance under some tensor products and some calculations

Sumit Kumar

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arXiv · 2601.05154

On stability of distance under some tensor products and some calculations

Sumit Kumar

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Abstract

We prove that the Kadison-Kastler and Christensen distances are stable under the Banach space injective tensor product (resp., the Banach space projective tensor product) of a Banach space with any unital commutative $C^*$-algebra (resp., of a $C^*$-algebra with any unital $C^*$-algebra). Apart from these stability results, we make some explicit calculations of the Kadison-Kastler, Christensen and Mashood-Taylor distances between certain subalgebras of some crossed-product operator algebras.

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Sumit Kumar. 2026-01-08. On stability of distance under some tensor products and some calculations. https://arxiv.org/abs/2601.05154

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