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ISSN 1449-5910  

 

Paper Information

Paper Title:

Preserver of Local Spectrum of Skew-product Operators

Author(s):

Rohollah Parvinianzadeh1,*, Meysam Asadipour2 and Jumakhan Pazhman3

1Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: r.parvinian@yu.ac.ir

2Department of Mathematics,
College of Sciences,
University of Yasouj,
Yasouj, 75918-74934,
Iran.
E-mail: Asadipour@yu.ac.ir

3Department of Mathematics,
Ghor Institute of higher education,
Afghanistan.
E-mail: jumapazhman@gmail.com

Abstract:

Let H and K be infinite-dimensional complex Hilbert spaces, and B(H) (resp. B(K)) be the algebra of all bounded linear operators on H (resp. on K). For an operator T B(H) and a vector h H, let σT(h) denote the local spectrum of T at h. For two nonzero vectors h0 H and k0 K, we show that if two maps φ1 and φ2 from B(H) into B(K) satisfy

σφ1(T)φ2(S)*(k0)= σTS*(h0})

for all T, S B(H), and their range containing all operators of rank at most two, then there exist bijective linear maps P : H K and Q : K H such that φ1(T) = PTQ and φ2(T)* =Q-1T*P-1 for all T B(H). Also, we obtain some interesting results in this direction.

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