Spectral radius formula for commuting Hilbert space operators

extend numerical radius for adjointable operators on Hilbert C^* -modules

In this paper, a new definition of numerical radius for adjointable operators in Hilbert -module space will be introduced. We also give a new proof of numerical radius inequalities for Hilbert space operators.

m-Isometric Commuting Tuples of Operators on a Hilbert Space

We consider a generalization of isometric Hilbert space operators to the multivariable setting. We study some of the basic properties of these tuples of commuting operators and we explore several examples. In particular, we show that the d-shift, which is important in the dilation theory of d-contractions (or row contractions), is a d-isometry. As an application of our techniques we prove a the...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...  

A formula for the inner spectral radius

Some Lower Bounds for the Numerical Radius of Hilbert Space Operators

We show that if T is a bounded linear operator on a complex Hilbert space, then 1 2 ‖T‖ ≤ √ w2(T ) 2 + w(T ) 2 √ w2(T )− c2(T ) ≤ w(T ), where w(·) and c(·) are the numerical radius and the Crawford number, respectively. We then apply it to prove that for each t ∈ [0, 12 ) and natural number k, (1 + 2t) 1 2k 2 1 k m(T ) ≤ w(T ), where m(T ) denotes the minimum modulus of T . Some other related ...