2022/10/12 by Seal, Susmita, Basu, Sudeshna, Guerrero, Julio Becerra +1
#46B20 #46B28 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2210.05887
In this work, we study non-rough norms in L(X,Y), the space of bounded linear operators between Banach spaces X and Y. We prove that L(X,Y) has non-rough norm if and only if X* and Y have non-rough norm. We show that the injective tensor product of X and Y has non-rough norm if and only if both X and Y have non-rough norm. We also give an example to show that non-rough norms are not stable under projective tensor product. We also study a related concept namely the small diameter properties in the context of L(X,Y)*. These results leads to a discussion on stability of the small diameter properties for projective and injective tensor product spaces.