BISHOP'S PROPERTY AND WEIGHTED CONDITIONAL TYPE OPERATORS IN k-QUASI CLASS A n
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.
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- ISSN: 2146-1147
- Başlangıç: 2010
- Yayıncı: Turkic World Mathematical Society
Sayıdaki Diğer Makaleler
M. UNVER, G. OZCELİK, M. OLGUN
C. YAMAÇ, M. S. OZ, I. N. CANGUL
K. DOGAN, F. GURSOY, V. KARAKAYA
S. GUMGUM, N. B. SAVASANERİL, O. K. KURKCU, M. SEZER