# Daugavet centers and direct sums of Banach spaces

Open Mathematics (2010)

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

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topTetiana 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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