Daugavet centers and direct sums of Banach spaces

Tetiana Bosenko

Open Mathematics (2010)

  • Volume: 8, Issue: 2, page 346-356
  • ISSN: 2391-5455

Abstract

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A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X 1⊕F X 2 of two Banach spaces X 1 and X 2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X 1 and X 2 there exists a Daugavet center acting from X 1⊕F X 2, and the class of those F such that for some pair of spaces X 1 and X 2 there is a Daugavet center acting into X 1⊕F X 2. We also present several examples of such Daugavet centers.

How to cite

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Tetiana Bosenko. "Daugavet centers and direct sums of Banach spaces." Open Mathematics 8.2 (2010): 346-356. <http://eudml.org/doc/268970>.

@article{TetianaBosenko2010,
abstract = {A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X 1⊕F X 2 of two Banach spaces X 1 and X 2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X 1 and X 2 there exists a Daugavet center acting from X 1⊕F X 2, and the class of those F such that for some pair of spaces X 1 and X 2 there is a Daugavet center acting into X 1⊕F X 2. We also present several examples of such Daugavet centers.},
author = {Tetiana Bosenko},
journal = {Open Mathematics},
keywords = {Daugavet center; Daugavet property; Direct sum of Banach spaces; direct sum of Banach spaces},
language = {eng},
number = {2},
pages = {346-356},
title = {Daugavet centers and direct sums of Banach spaces},
url = {http://eudml.org/doc/268970},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Tetiana Bosenko
TI - Daugavet centers and direct sums of Banach spaces
JO - Open Mathematics
PY - 2010
VL - 8
IS - 2
SP - 346
EP - 356
AB - A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X 1⊕F X 2 of two Banach spaces X 1 and X 2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X 1 and X 2 there exists a Daugavet center acting from X 1⊕F X 2, and the class of those F such that for some pair of spaces X 1 and X 2 there is a Daugavet center acting into X 1⊕F X 2. We also present several examples of such Daugavet centers.
LA - eng
KW - Daugavet center; Daugavet property; Direct sum of Banach spaces; direct sum of Banach spaces
UR - http://eudml.org/doc/268970
ER -

References

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