Advances in Operator Theory最新文献

The central focus of this paper is the analysis of optimal dual frames for a given frame as well as optimal dual pairs, in light of a probability model-based erasure during the transmission of the frame coefficients corresponding to the data. We consider these two broad and different contexts of the erasure problem and analyze each of them, with the optimality measure taken to be the spectral radius as well as the operator norm of the associated error operators.

In this research, we analyze the existence of infinite sequences of ordered solutions for a class of non-local elliptic problem with Dirichlet boundary condition. The primary techniques employed consist of topological degree theory for mappings of type (S_+) and minimization arguments in a fractional Orlicz–Sobolev space. Our main results generalize some recent findings in the literature to non-smooth cases.

We follow several approaches in nonlinear spectral theory and determine the various spectral forms for the nonlinear weighted superposition operator on Fock spaces. The results show that most of the forms introduced so far coincide and contain singeltons. The classical, asymptotic, and connected eigenvalues, and some numerical ranges of the operator are also identified. We further prove that the operator is both linear and odd asymptotically with respect to the pointwise multiplication operator on the spaces.

In this paper, using Hardy–Littlewood maximal function, we deal with the boundedness of the (psi )-Riemann–Liouville in Lebesgue and weighted Lebesgue space in the real line. Moreover, we consider the boundedness of (psi )-Riemann–Liouville tempered fractional integrals in weighted Lebesgue space in the real line.

In this paper, we obtain some new matrix inequalities involving Hadamard product. Also, some Hadamard product inequalities for accretive matrices involving the matrix means, positive unital linear maps, and matrix concave functions are investigated.

Let S be a n-by-n truncated shift whose numerical radius equal one. First, Cassier et al. (J Oper Theory 80(2):453–480, 2018) proved that the Harnack part of S is trivial if (n=2), while if (n=3), then it is an orbit associated with the action of a group of unitary diagonal matrices; see Theorem 3.1 and Theorem 3.3 in the same paper. Second, Cassier and Benharrat (Linear Multilinear Algebra 70(5):974–992, 2022) described elements of the Harnack part of the truncated n-by-n shift S under an extra assumption. In Sect. 2, we present useful results in the general finite-dimensional situation. In Sect. 3, we give a complete description of the Harnack part of S for (n=4), the answer is surprising and instructive. It shows that even when the dimension is an even number, the Harnack part is bigger than conjectured in Question 2 and we also give a negative answer to Question 1 (the two questions are contained in the last cited paper), when (rho =2).

In this article, we generalize an approximation result known for entropy numbers of operators. We show that the entropy numbers of a bounded linear operator can be approximated by those of certain truncations of the operator under very general assumptions. Using the relation between the entropy numbers and the inner entropy numbers of bounded sets, we derive estimates for entropy numbers of bounded linear operators. We also obtain new estimates for specific types of operators, including the diagonal operators between sequence spaces, and use these estimates to illustrate the convergence result proved.

The Krein transform is the real counterpart of the Cayley transform and gives a one-to-one correspondence between the positive relations and symmetric contractions. It is treated with a slight variation of the usual one, resulting in an involution for linear relations. On the other hand, a semi-bounded linear relation has closed semi-bounded symmetric extensions with semi-bounded selfadjoint extensions. A self-consistent theory of semi-bounded symmetric extensions of semi-bounded linear relations is presented. Using the Krein transform, a formula of positive extensions of quasi-null relations is provided.

We prove that the closure of the numerical range of a ((n+1))-periodic and ((2m+1))-banded Toeplitz operator can be expressed as the closure of the convex hull of the uncountable union of numerical ranges of certain symbol matrices. In contrast to the periodic 3-banded (or tridiagonal) case, we show an example of a 2-periodic and 5-banded Toeplitz operator such that the closure of its numerical range is not equal to the numerical range of a single finite matrix.