Spectral Properties of k-Quasi Parahyponormal Operators

Authors

  • D. Senthilkumar Post Graduate and Research Department of Mathematics, Govt. Arts College (Autonomous), Coimbatore 18
  • S. Parvatham Post Graduate and Research Department of Mathematics, Govt. Arts College (Autonomous), Coimbatore 18

DOI:

https://doi.org/10.26713/jims.v9i3.952

Keywords:

Parahyponormal operator, Approximate point spectrum and Joint approximate point spectrum

Abstract

In this paper, we prove some basic properties of k-quasi-parahyponormal operators and spectrum of class of k-quasi-parahyponormal operators is continuous. Also, we proved the non zero points of its approximate point spectrum and joint approximate point spectrum are identical.

Downloads

References

A. Aluthge, On p-hyponormal operators for (0

S.K. Berberian, Approximate proper vectors, Proc. Amer. Math. Soc. 13 (1962), 111 – 114, doi:10.2307/2033783.

J.B. Conway and B.B. Morrel, Operators that are points of spectral continuity, Integr. Equ. Oper. Theory 2 (1979), 174 – 198 doi:10.1007/BF01682733.

S.V. Djordjevic, Continuity of the essential spectrum in the class of quasihyponormal operators, Vesnik Math. 50 (1998), 71 – 74, elib.mi.sanu.ac.rs/files/journals/mv/211/mv983402.pdf.

B.P. Duggal, I.H. Jeon and I.H. Kim, Continuity of the spectrum on a class of upper triangular operator matrices, J. Math. Anal. Appl. 370 (2010), 584 – 587 http://dx.doi.org/10.1016/j.jmaa.2010.04.068.

B.P. Duggal, I.H. Jeon and I.H. Kim, On (^*)-paranormal contractions and properties for *-class A operators, Linear Algebra Appl. 436 (2012), 954 – 962 http://dx.doi.org/10.1016/j.laa.2011.06.002.

T. Furuta, On the class of paranormal operators, Proc. Jpn. Acad. 43 (1967), 594 – 598, https://projecteuclid.org/download/pdf1/euclid.pja/1195521514.

T. Furuta, Invitation to Linear Operators, Taylor and Francis, London (2001).

P.R. Halmos, A Hilbert Space Problem Book, Springer-Verlag, New York (1982).

Y.M. Han and A.H. Kim, A note on (^*)-paranormal operators, Integr. Equ. Oper. Theory 49(4) (2004), 435 – 444 doi:10.1007/s00020-002-1217-5.

J.K. Han and H.Y. Lee, Invertible completions of 2*2 upper triangular operator matrices, Proc. Amer. Math. Soc. 128 (1999), 119 – 123, www.ams.org/proc/2000-128-01/S0002-9939-99.../S0002-9939-99-04965-5.pdf

I.S. Hwang and W.Y. Lee, The spectrum is continuous on the set of p-hyponormal operators, Math. Z. 235 (2000), 151 – 157 doi:10.1007/s002090000128

I.S. Hwang and W.Y. Lee, On the continuity of spectra of Toeplitz operators, Arch. Math. 70 (1998), 66 – 73 doi:10.1007/s000130050166.

M. Mahmoud Kutkut, On the classes of Parahyponormal operator, Jour. Math. Sci. 4(2) (1993), 73 – 88.

S. Mecheri, On a new class of operators and Weyl type theorems, Filomat 27 (2013), 629 – 636, www.doiserbia.nb.rs/ft.aspx?id=0354-51801304629M.

P. Pagacz, On Wold-type decomposition, Linear Algebra Appl. 436 (2012), 3605 – 3071.

J.L. Shen and A. Chen, The spectrum properties of quasi-(^*)-paranormal operators, Chinese Annals of Math. (in Chinese) 34(6) (2013), 663 – 670.

Downloads

Published

2017-10-30
CITATION

How to Cite

Senthilkumar, D., & Parvatham, S. (2017). Spectral Properties of k-Quasi Parahyponormal Operators. Journal of Informatics and Mathematical Sciences, 9(3), 855–862. https://doi.org/10.26713/jims.v9i3.952

Issue

Section

Research Article