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Year 2020, Volume: 10 Issue: 1, 241 - 250, 01.01.2020

Abstract

References

  • Ando, T., (1972), Operators with a norm condition, Acta Sci. Math. (Szeged), 33, pp. 169-178.
  • Cho, M., Tanahashi, K., Isolated point of spectrum of p-hyponormal operator, loghyponormal opera- tors, preprint. Duggal, B. P., (2000), Tensor products of operators-strong stability and p-hyponormality, Glasg. Math. J., 42, pp. 371-381.
  • Duggal, B. P., Jeon, I. H., Kim, I. H., (2012), On *-paranormal contractions and property for *-class
  • A operators, Linear Algebra Appl., 436, pp. 954-962. Estaremi, Y., (2015), Some classes of weighted conditional type operators and their spectra, Positivity, , pp. 83-93.
  • Estaremi, Y., Jabbarzadeh, M. R., (2013), Weighted Lambert type operator on Lpspaces, Oper. Matrices., 1, pp. 101-116.
  • Gao, F. G., Li, X. C., (2014), Tensor products and the spectral continuity for k-quasi-*-class A operators, Banach J. Math. Anal., 8, pp. 47-54.
  • Herron, J., (2011), Weighted conditional expectation operators, Oper. Matrices, 5, pp. 107-118.
  • Hou, J. C., (1993), On tensor products of operators, Acta Math. Sin. (N. S.), 9, pp. 195-202.
  • Hoxha, I., Braha, N. L., (2014), On k-quasi class A*operators, Bulletin of Mathematical Analysis and Applications, 6, pp. 23-33.
  • Jeon, I. H., Kim, I. H., (2006), On operators satisfying T*|T2|T ≥ T*|T |2T , Linear Algebra Appl., , pp. 854-862.
  • Jeon, I. H., Kim, I. H., (2006), On operators satisfying T*|T|T ≥ T*|T |T , Linear Algebra Appl., , pp. 854-862.
  • Kubrusly, C. S., (2012), Spectral theory of operators on Hilbert spaces, Birkhuser/Springer, New York.
  • Mecheri, S., (2012), Isolated points of spectrum of k-quasi - *- class A operators, Studia Mathematica , pp. 87-96.
  • Rao, M. M., (1993), Conditional measure and applications, Marcel Dekker, New York.
  • Sait, T., (1972), Hyponormal operators and related topics, Lectures on operator algebras (dedicated to the memory of David M. Topping; Tulane Univ. Ring and Operator Theory Year, 19701971, Vol. II), pp. 533–664.
  • Stampfli, J. G., (1965), Hyponormal operators and spectral density, Trans. Amer. Math. Soc., 117, pp. 469-476.
  • Stochel, J., (1996), Seminormality of operators from their tensor product, Proc. Amer. Math. Soc., , pp. 135-140.
  • Tanahashi, K., Jeon, I. H., Kim, I. H., Uchiyama, A., (2009), Quasinilpotent part of class A or (p, k)-quasihyponormal operators, Oper. Theory Adv. Appl. 187, pp. 199-210.
  • Uchiyama, A., (2006), On the isolated points of the spectrum of paranormal operators, Integral
  • Equations Operator Theory 55, pp. 145-151. Uchiyama, A., Tanahashi, K., (2002), On the Riesz idempotent of class A operator, Math Inequal Appl, 5, pp. 291-298.

BISHOP'S PROPERTY AND WEIGHTED CONDITIONAL TYPE OPERATORS IN k-QUASI CLASS A n

Year 2020, Volume: 10 Issue: 1, 241 - 250, 01.01.2020

Abstract

An operator T is said to be k-quasi class A ∗ n operator if T ∗k  |T n+1| 2 n+1 − |T ∗ | 2  T k ≥ 0, for some positive integers n and k. In this paper, we prove that the k-quasi class A ∗ n operators have Bishop, s property β . Then, we give a necessary and sufficient condition for T ⊗S to be a k-quasi class A ∗ n operator, whenever T and S are both non-zero operators. Moreover, it is shown that the Riesz idempotent for a non-zero isolated point λ0 of a k-quasi class A ∗ n operator T say Ri, is self-adjoint and ran Ri = ker T −λ0 = ker T −λ0 ∗ . Finally, as an application in the last section, a necessary and sufficient condition is given in such a way that the weighted conditional type operators on L 2 Σ , defined by Tw,u f := wE uf , belong to k-quasi- A ∗ n class.

References

  • Ando, T., (1972), Operators with a norm condition, Acta Sci. Math. (Szeged), 33, pp. 169-178.
  • Cho, M., Tanahashi, K., Isolated point of spectrum of p-hyponormal operator, loghyponormal opera- tors, preprint. Duggal, B. P., (2000), Tensor products of operators-strong stability and p-hyponormality, Glasg. Math. J., 42, pp. 371-381.
  • Duggal, B. P., Jeon, I. H., Kim, I. H., (2012), On *-paranormal contractions and property for *-class
  • A operators, Linear Algebra Appl., 436, pp. 954-962. Estaremi, Y., (2015), Some classes of weighted conditional type operators and their spectra, Positivity, , pp. 83-93.
  • Estaremi, Y., Jabbarzadeh, M. R., (2013), Weighted Lambert type operator on Lpspaces, Oper. Matrices., 1, pp. 101-116.
  • Gao, F. G., Li, X. C., (2014), Tensor products and the spectral continuity for k-quasi-*-class A operators, Banach J. Math. Anal., 8, pp. 47-54.
  • Herron, J., (2011), Weighted conditional expectation operators, Oper. Matrices, 5, pp. 107-118.
  • Hou, J. C., (1993), On tensor products of operators, Acta Math. Sin. (N. S.), 9, pp. 195-202.
  • Hoxha, I., Braha, N. L., (2014), On k-quasi class A*operators, Bulletin of Mathematical Analysis and Applications, 6, pp. 23-33.
  • Jeon, I. H., Kim, I. H., (2006), On operators satisfying T*|T2|T ≥ T*|T |2T , Linear Algebra Appl., , pp. 854-862.
  • Jeon, I. H., Kim, I. H., (2006), On operators satisfying T*|T|T ≥ T*|T |T , Linear Algebra Appl., , pp. 854-862.
  • Kubrusly, C. S., (2012), Spectral theory of operators on Hilbert spaces, Birkhuser/Springer, New York.
  • Mecheri, S., (2012), Isolated points of spectrum of k-quasi - *- class A operators, Studia Mathematica , pp. 87-96.
  • Rao, M. M., (1993), Conditional measure and applications, Marcel Dekker, New York.
  • Sait, T., (1972), Hyponormal operators and related topics, Lectures on operator algebras (dedicated to the memory of David M. Topping; Tulane Univ. Ring and Operator Theory Year, 19701971, Vol. II), pp. 533–664.
  • Stampfli, J. G., (1965), Hyponormal operators and spectral density, Trans. Amer. Math. Soc., 117, pp. 469-476.
  • Stochel, J., (1996), Seminormality of operators from their tensor product, Proc. Amer. Math. Soc., , pp. 135-140.
  • Tanahashi, K., Jeon, I. H., Kim, I. H., Uchiyama, A., (2009), Quasinilpotent part of class A or (p, k)-quasihyponormal operators, Oper. Theory Adv. Appl. 187, pp. 199-210.
  • Uchiyama, A., (2006), On the isolated points of the spectrum of paranormal operators, Integral
  • Equations Operator Theory 55, pp. 145-151. Uchiyama, A., Tanahashi, K., (2002), On the Riesz idempotent of class A operator, Math Inequal Appl, 5, pp. 291-298.
There are 20 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

M. R. Azimi This is me

I. Akbarbaglu This is me

F. Abedi This is me

Publication Date January 1, 2020
Published in Issue Year 2020 Volume: 10 Issue: 1

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