ON POSITIVE-NORMAL OPERATORS

Lecture 18 : Normal operators , the spectral theorems , isometries , and positive operators ( 1 )

Remarks on Hyponormal Operators and Almost Normal Operators

In 1984 M. Putinar proved that hyponormal operators are subscalar operators of order two. The proof provided a concrete structure of such operators. We will use this structure to give a sufficient condition for hyponormal operators T with trace-class commutator to admit a direct summand S so that T ⊕ S is the sum of a normal operator and a HilbertSchmidt operator. We investigate what this suffi...

On some fuzzy positive and linear operators

The purpose of this work is to show that fuzzy Bernstein-Stancu operators introduced in [3] satisfy an A-statistical version of fuzzy Korovkin theorem. Some properties of these operators are also proved. An example of new fuzzy positive and linear operators is presented.

Norms of Positive Operators on LP-Spaces

Let 0 < T: LP(Y, v) -+ Lq(X, ) be a positive linear operator and let HITIP ,q denote its operator norm. In this paper a method is given to compute 1Tllp, q exactly or to bound 11Tllp q from above. As an application the exact norm 11VIlp,q of the Volterra operator Vf(x) = fo f(t)dt is computed.

Norms of Positive Operators on L-spaces

Let 0 ≤ T : L(Y, ν) → L(X,μ) be a positive linear operator and let ‖T‖p,q denote its operator norm. In this paper a method is given to compute ‖T‖p,q exactly or to bound ‖T‖p,q from above. As an application the exact norm ‖V ‖p,q of the Volterra operator V f(x) = ∫ x 0 f(t)dt is computed. Department of Mathematics, University of South Carolina, Columbia, SC 29208 1991 Mathematics Subject Classi...