New York Journal of Mathematics
Volume 28 (2022), 1656-1666


Carlos S. Kubrusly

Restriction of uniform crossnorms

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Published: December 7, 2022.
Keywords: Bounded linear operators, tensor product, uniform crossnorms.
Subject [2010]: 47A80, 46M05.

Consider the space B[X ⊗ Y] of operators on the tensor product X ⊗ Y of normed spaces X and Y equipped with a uniform crossnorm. Take the induced uniform norm on B[X ⊗ Y] and consider its restriction to the tensor product B[X] ⊗ B[Y] of the algebra of operators B[X] and B[Y]. It is proved that such a restriction is a reasonable crossnorm on B[X] ⊗ B[Y].


The author thanks a referee for suggestions to improve the paper which were included in Remarks 4.2 and 4.3; especially for calling his attention to the inequality that opens the argument of Remark 4.3.

Author information

Carlos S. Kubrusly:
Department of Electrical Engineering
Catholic University of Rio de Janeiro, Brazil