We consider separately radial (with corresponding group ${𝕋}^n$) and radial (with corresponding group $\mathrm{U}\left(n\right))$ symbols on the projective space ${\mathbb{P}}^n\left(ℂ\right)$, as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the $C^{*}$-algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the...

An eigenvalue criterion for hypercyclicity due to the first author is improved. As a consequence, some new sufficient conditions for a sequence of infinite order linear differential operators to be hypercyclic on the space of holomorphic functions on certain domains of ${ℂ}^N$ are shown. Moreover, several necessary conditions are furnished. The equicontinuity of a family of operators as above is also studied, and it is characterized if the domain is ${ℂ}^N$. The results obtained extend or improve earlier work...

Complete and σ-complete Boolean algebras of projections acting in a Banach space were introduced by W. Bade in the 1950's. A basic fact is that every complete Boolean algebra of projections is necessarily a closed set for the strong operator topology. Here we address the analogous question for σ-complete Boolean algebras: are they always a sequentially closed set for the strong operator topology? For the atomic case the answer is shown to be affirmative. For the general case, we develop criteria...

Under regularity assumptions, we establish a sharp large deviation principle for Hermitian quadratic forms of stationary Gaussian processes. Our result is similar to the well-known Bahadur-Rao theorem [2] on the sample mean. We also provide several examples of application such as the sharp large deviation properties of the Neyman-Pearson likelihood ratio test, of the sum of squares, of the Yule-Walker estimator of the parameter of a stable autoregressive Gaussian process, and finally of the empirical...

The present paper is a continuation of [23], from which we know that the theory of traces on the Marcinkiewicz operator ideal $\left(H\right):=T\in \left(H\right):su{p}_{1\le m<\infty }1/(logm+1){\sum }_{n=1}^{m}aₙ\left(T\right)<\infty$ can be reduced to the theory of shift-invariant functionals on the Banach sequence space $\left(\mathbb{N}₀\right):=c=\left({\gamma }_l\right):su{p}_{0\le k<\infty }1/(k+1){\sum }_{l=0}^k\left|{\gamma }_l\right|<\infty$. The final purpose of my studies, which will be finished in [24], is the following. Using the density character as a measure, I want to determine the size of some subspaces of the dual *(H). Of particular interest are the sets formed by the Dixmier traces and the Connes-Dixmier traces...

Let X be an infinite-dimensional Banach space, and B(X) the algebra of all bounded linear operators on X. Then ϕ: B(X) → B(X) is a bijective similarity-preserving linear map if and only if one of the following holds: (1) There exist a nonzero complex number c, an invertible bounded operator T in B(X) and a similarity-invariant linear functional h on B(X) with h(I) ≠ -c such that $\varphi \left(A\right)=cTA{T}^{-1}+h\left(A\right)I$ for all A ∈ B(X). (2) There exist a nonzero complex number c, an invertible bounded linear operator T: X* → X and a...

We construct in this paper some simultaneous projective resolutions of the identity operator which we later use to obtain certain new results on quasi-complementation property and Markushevich bases.

The purpose of this paper is to give singular integral models for p-hyponormal operators and apply them to the Riemann-Hilbert problem.

In 1968, Gohberg and Krupnik found a Fredholm criterion for singular integral operators of the form aP + bQ, where a,b are piecewise continuous functions and P,Q are complementary projections associated to the Cauchy singular integral operator, acting on Lebesgue spaces over Lyapunov curves. We extend this result to the case of Nakano spaces (also known as variable Lebesgue spaces) with certain weights having finite sets of discontinuities on arbitrary Carleson curves.