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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 28, Issue 2, Pages 305 - 317 (February 2008)


A NOTE ON SIMILARITY, ALMOST-SIMILARITY AND EQUIVALENCE OF OPERATORS

B. M. Nzimbi (Kenya), G. P. Pokhariyal (Kenya) and J. M. Khalagai (Kenya)

Received May 29, 2007; Revised October 12, 2007

References:



[1] C. Apostol, C. Foiaş and D. Voiculescu, Some results on non-quasitriangular operators, IV, Rev. Roumaine Math. Pures Appl. 18 (1973), 487-514.

[2] C. Apostol, C. Foiaş and D. Voiculescu, On the norm-closure of nilpotents, II, Rev. Roumaine Math. Pures Appl. 19 (1974), 549-557.

[3] L. A. Fialkow, The similarity orbit of a normal operator, Trans. Amer. Math. Soc. 210 (1975), 129-137.

[4] D. Hadwin, Strongly quasidiagonal -algebras, J. Operator Theory 18 (1987), 3-18.

[5] P. R. Halmos, Quasitriangular operators, Acta Sci. Math. (Szeged) 29 (1968), 283-293.

[6] D. A. Herrero, Quasidiagonality, similarity and approximation by nilpotent operators, Indiana Univ. Math. J. 30 (1981), 199-233.

[7] D. A. Herrero, On quasidiagonal weighted shifts and approximation of operators, Indiana Univ. Math. J. 33 (1984), 549-571.

[8] A. A. S. Jibril, On almost similar operators, Arabian J. Sci. Engrg. 21 (1996), 443-449.

[9] L. W. Johnson, R. D. Reiss and J. T. Arnold, Introduction to Linear Algebra, 2nd ed., Addison-Wesley, 1989.

[10] C. S. Kubrusly, An Introduction to Models and Decompositions in Operator Theory, Birkhäuser, 1997.

[11] R. Smucker, Quasidiagonal and Quasitriangular Operators, Dissertation, Indiana University, 1973.

[12] A. B. Thaheem, Decomposition of a von Neumann algebra relative to a *-automorphism, Proc. Edinb. Math. Soc. (2) 22 (1979), 9-10.

Keywords and phrases: almost-similar, similar, hermitian, isometric.

 


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