New characterizations of asymptotic stability for evolution families on Banach spaces.
Noncommutative fractional integrals
Let ℳ be a hyperfinite finite von Nemann algebra and be an increasing filtration of finite-dimensional von Neumann subalgebras of ℳ. We investigate abstract fractional integrals associated to the filtration . For a finite noncommutative martingale adapted to and 0 < α < 1, the fractional integral of x of order α is defined by setting for an appropriate sequence of scalars. For the case of a noncommutative dyadic martingale in L₁() where is the type II₁ hyperfinite factor equipped...
Norm attaining operators
Norm inequalities for integral operators on cones
Norm inequalities for partitioned operators and an application.
Norm inequalities for sequences of operators related to the Schwarz inequality.
Norm inequalities in star algebras.
Norm inequalities relating singular integrals and the maximal function
Norms of certain operators on weighted spaces and Lorentz sequence spaces.
Norms of certain rational functions of a matrix and Schur's criterion for polynomials
Norms of inverses, spectra, and pseudospectra of large truncated Wiener-Hopf operators and Toeplitz matrices.
Notes on some spectral radius and numerical radius inequalities
We prove numerical radius inequalities for products, commutators, anticommutators, and sums of Hilbert space operators. A spectral radius inequality for sums of commuting operators is also given. Our results improve earlier well-known results.
Numerical radius and operator norm inequalities.
Numerical radius inequalities for 2 × 2 operator matrices
We derive several numerical radius inequalities for 2 × 2 operator matrices. Numerical radius inequalities for sums and products of operators are given. Applications of our inequalities are also provided.
Numerical radius inequalities for Hilbert space operators
It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1/4 ||A*A + AA*|| ≤ (w(A))² ≤ 1/2 ||A*A + AA*||, where w(·) and ||·|| are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities 1/2 ||A|| ≤ w(A) ≤ || A||. Numerical radius inequalities for products and commutators of operators are also obtained.
Numerical radius inequalities for Hilbert space operators. II
We give several sharp inequalities involving powers of the numerical radii and the usual operator norms of Hilbert space operators. These inequalities, which are based on some classical convexity inequalities for nonnegative real numbers and some operator inequalities, generalize earlier numerical radius inequalities.