论文信息 - Linear maps preserving essential spectral functions and closeness of operator ranges

Linear maps preserving essential spectral functions and closeness of operator ranges

Let H be an infinite‐dimensional complex Hilbert space and ℬ(H) the algebra of all bounded linear operators on H. Some characterizations are obtained of linear maps Φ on ℬ(H) preserving essential spectral functions such as the intersection of left essential spectrum and right essential spectrum of operators, preserving Fredholm operators, and preserving semi‐Fredholm operators, and preserving closeness of operator ranges. A result of Mbekhta, Rodman and Šemrl (Integral Equations Operator Theory 55 (2006) 93‐109) on generalized invertibility preserving linear maps is improved.

J. Hou | Jianlian Cui

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