For non-reflexive Banach spaces X, Y, for a very smooth point in the space of compact linear operators K(X, Y), we give several sufficient conditions for the adjoint to be a very smooth point in K(Y *,X*). We exhibit a new class of extreme points in the dual unit ball of injective product spaces. These ideas are also related to Birkhoff-James orthogonality in spaces of operators.
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Communicated by L. Molnár
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Rao, T.S.S.R.K. Geometry of spaces of compact operators. ActaSci.Math. 85, 495–505 (2019). https://doi.org/10.14232/actasm-018-809-2
AMS Subject Classification (2000)
Key words and phrases
- smooth points
- very smooth points
- adjoints of operators
- spaces of operators
- essential norm
- injective and projective tensor product spaces