WEYL@S THEOREMS FOR POSINORMAL OPERATORS

Saturation theorems for diseretized linear operators

There is a well developed theory of saturation for positive convolution operators on C*, the space of 2n-periodic and continuous functions. Up until recently, this was suitable to handle almost all the important approximation processes on C*. Now, however, some new and interesting sequences of operators have been obtained for C* by discretizing convolution operators [1], [5]. Such a discretized...

Fixed point theorems for sums of operators

Spectral Mapping Theorems for Hyponormal Operators

Let T=H+iK be hyponormal and Q be a strictly monotone increasing continuous function on s(H ). We define ~ Q(T ) by ~ Q(T )=Q(H )+iK. In this paper, we show that if z is an isolated eigenvalue of ~ Q(T ), then the corresponding Riesz projection is self-adjoint. Also we introduce Xia spectrum and study the existence of an invariant subspace of an operator ~ Q(T ).

Enclosure Theorems for Eigenvalues of Elliptic Operators

are to be considered when the coefficients a,-,-, b, and c are continuous real-valued functions with &=^0, c>0 in En. The ellipticity of L implies that the symmetric matrix (a,,) is everywhere positive definite. A "solution" u of Lu = 0 is supposed to be of class C1 and all derivatives involved in (1.1) are supposed to exist, be continuous, and satisfy Lu = 0 at every point. The eigenvalue prob...

Direct Approximation Theorems for Discrete Type Operators

In the present paper we prove direct approximation theorems for discrete type operators (Lnf)(x) = ∞ ∑ k=0 un,k(x)λn,k(f), f ∈ C[0,∞), x ∈ [0,∞) using a modified K−functional. As applications we give direct theorems for Baskakov type operators, Szász-Mirakjan type operators and Lupaş operator.