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Geometry of spaces of compact operators

Acta Scientiarum Mathematicarum volume 85, pages 495–505 (2019)Cite this article

Abstract

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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Authors and Affiliations

  1. Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, R. V. College P.O., Bangalore, 560059, India

    T. S. S. R. K. Rao

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  1. T. S. S. R. K. Rao
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Correspondence to T. S. S. R. K. Rao.

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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

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  • DOI: https://doi.org/10.14232/actasm-018-809-2

AMS Subject Classification (2000)

  • 47L05
  • 46B28
  • 46B25

Key words and phrases

  • smooth points
  • very smooth points
  • adjoints of operators
  • spaces of operators
  • essential norm
  • injective and projective tensor product spaces