Linear maps preserving equivalence or asymptotic equivalence on Banach space

Linear maps preserving equivalence or asymptotic equivalence on Banach space

Let XX be a complex Banach space with dimension at least two and B(X)B\left(X) the algebra of all bounded linear operators on XX. We show that a bijective linear map Φ\Phi preserves asymptotic equivalence if and only if it preserves equivalence, and in turn, if and only if there exist invertible bo...

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Bibliographic Details
Main Authors: Qin Zijie, Chen Lin
Format: Article
Language:English
Published: De Gruyter 2023-10-01
Series:Open Mathematics
Subjects:
linear preservers
asymptotic equivalence
equivalence relations
banach spaces
47b49
Online Access:https://doi.org/10.1515/math-2023-0125

Internet

https://doi.org/10.1515/math-2023-0125

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