Research Article Spectrum of Class wF(p,r,q) Operators
نویسندگان
چکیده
This paper discusses some spectral properties of class wF(p,r,q) operators for p > 0, r > 0, p + r ≤ 1, and q ≥ 1. It is shown that if T is a class wF(p,r,q) operator, then the Riesz idempotent Eλ of T with respect to each nonzero isolated point spectrum λ is selfadjoint and Eλ = ker(T − λ)= ker(T − λ)∗ . Afterwards, we prove that every class wF(p,r,q) operator has SVEP and property (β), andWeyl’s theorem holds for f (T) when f ∈H(σ(T)).
منابع مشابه
POWERS OF CLASS wF ( p , r , q ) OPERATORS
This paper is to discuss powers of class wF (p, r, q) operators for 1 ≥ p > 0, 1 ≥ r > 0 and q ≥ 1; and an example is given on powers of class wF (p, r, q) operators.
متن کاملOn the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators
In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...
متن کاملCertain subclass of $p$-valent meromorphic Bazilevi'{c} functions defined by fractional $q$-calculus operators
The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...
متن کاملLp Spectral Independence of Elliptic Operators via Commutator Estimates
Let fT p : q 1 p q 2 g be a family of consistent C 0 semigroups on L p ((), with q 1 ; q 2 2 1; 1) and R n open. We show that certain commutator conditions on T p and on the resolvent of its generator A p ensure the p independence of the spectrum of A p for p 2 q 1 ; q 2 ]. Applications include the case of Petrovskij correct systems with HH older continuous coeecients, Schrr odinger operators, ...
متن کاملSome inequalities involving lower bounds of operators on weighted sequence spaces by a matrix norm
Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma-trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the followinginequality:k Ax kv;B(q) L k x kv;B(p);where x 0 and x 2 lp(v;B) and also v = (vn)1n=1 is an increasing, non-negativesequence of real numbers. In this paper, we obtain a Hardy-type formula forLv;p;q;B(H), where H is the Hausdor matrix and 0 < q p 1. Also...
متن کامل