Let A be a positive (semidefinite) bounded linear operator on complex Hilbert space $$\big ({\mathcal {H}}, \langle \cdot , \rangle \big )$$ ( H ? · ? ) . The semi-inner product induced by is defined $${\langle x, y\rangle }_A := Ax, $$ x y : = for all $$x, y\in {\mathcal {H}}$$ ? and defines seminorm $${\Vert \Vert }_A$$ ? $${\mathcal This makes into semi-Hilbert space. For $$p\in [1,+\infty p...

We define the complete numerical radius norm for homomorphisms from any operator algebra into B(H), and show that this norm can be computed explicitly in terms of the completely bounded norm. This is used to show that if K is a complete Cspectral set for an operator T , then it is a complete M -numerical radius set, where M = 12 (C + C −1). In particular, in view of Crouzeix’s theorem, there is...

a‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. for this reason, many researchers have used various numerical methods to solve fuzzy linear systems. in this paper, we define the concepts of midpoint a...

We obtain inequalities involving numerical radius of a matrix A ∈ M n C. Using this result, we find upper bounds for zeros of a given polynomial. We also give a method to estimate the spectral radius of a given matrix A ∈ M n C up to the desired degree of accuracy.