SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2018 / Cilt: 47 - Sayı: 6

On m-quasi class A(k∗) and absolute-(k∗,m)-paranormal operators

Ilma HOXHA
Naim L. BRAHA
Kotaro TANAHASHİ
Pages
1564–1577
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Also, we consider the tensor product of m-quasi class A(k∗) operators.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce a new class of operators, called m-quasi class A(k∗) operators, which is a superclass of hyponormal operators and a subclass of absolute-(k∗,m)-paranormal operators.
📊
Key Findings & Data:We show that if T is m-quasi class A(k∗), then σnp(T) {0} = σp(T) {0}, σna(T) {0} = σa(T) {0} and T − µ has nite ascent for all µ ∈C.
💡
Conclusion & Impact:Also, we consider the tensor product of m-quasi class A(k∗) operators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper, we introduce a new class of operators, called m-quasi class A(k∗) operators, which is a superclass of hyponormal operators and a subclass of absolute-(k∗,m)-paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that if T is m-quasi class A(k∗), then σnp(T) {0} = σp(T) {0}, σna(T) {0} = σa(T) {0} and T − µ has nite ascent for all µ ∈C. Also, we consider the tensor product of m-quasi class A(k∗) operators.

🔖

Cite This Article

HOXHA, I., BRAHA, N. L., TANAHASHİ, K. (2022). On m-quasi class A(k∗) and absolute-(k∗,m)-paranormal operators. Hacettepe Journal of Mathematics and Statistics, Cilt: 47 - Sayı: 6, 1564–1577. https://ajindex.com/articles/529869

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. Aiena,P., Semi-Fredholm operators, perturbations theory and localized SVEP, XX Escuela Venezolana de Matematicas, Merida, Venezuela 2007.
  2. Aluthge, A., Wang, D., The joint approximate point spectrum of an operator, Hokkaido Math. J., 31 (2002), 187-197.
  3. Ando, T., Operators with a norm condition, Acta Sci. Math.(Szeged), 33, 169-178, 1972.
  4. Arora, S. C., Thukral, J. K., On a class of operators, Glas. Math. Ser. III, 21(41) no.2, 381-386, 1986.
  5. Duggal, B. P., Jeon, I. H., Kim, I. H., On -paranormal contractions and properties for -class A operators, Linear Alg. Appl. 436, 954-962, 2012.
  6. Furuta, T., On the class of paranormal operators, Proc. Japan Acad. 43, 594-598, 1967.
  7. Furuta, T., Ito, M., Yamazaki, T., A subclass of paranormal operators including class of log-hyponormal and several related classes, Sci. Math. 1, no.3, 389-403, 1998.
  8. Han, J. K., Lee, H. Y., Lee, W. Y., Invertible completions of 2 2 upper triangular operator matrices Proc. Amer. Math. Soc., 128, no.1, 119-123, 2000.
  9. Hansen, F., An operator inequality, Math. Ann. 246, 249-250, 1980.
  10. Kim, I. H., Weyl's theorem and tensor product for operators satisfying T kjT 2jT k T kjT j2T k, J. Korean Math. Soc. 47, No.2, 351-361, 2010.
  11. Kim, I. H., On spectral continuities and tensor products of operators, J. Chungcheong Math. Soc., 24, No.1, 113-119, 2011.
  12. McCarthy, C. A., cp, Israel J. Math. 5, 249-271, 1967.
  13. Panayappan, S., Radharamani, A., A Note on p- -paranormal Operators and Absolute- k - Paranormal Operators, Int. J. Math. Anal. 2, no.25-28, 1257-1261, 2008.
  14. Saito, T., Hyponormal operators and Related topics, Lecture notes in Math., Springer-Verlag, 247, 1971.
  15. Stochel, J., Seminormality of operators from their tensor products, Proc. Amer. Math. Soc., 124, 435-440, 1996