Remarks on a Question of Bourin for Positive Semidefinite Matrices

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Norm inequalities for positive definite matrices related to a question of Bourin

Amer Darweesh et al.

Summary: This statement provides a norm inequality for matrices A and B of the same size, when A and B are positive definite and satisfy certain conditions on their spectra.

LINEAR & MULTILINEAR ALGEBRA (2023)

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Positively p-nuclear operators, positively p-integral operators and approximation properties

Dongyang Chen et al.

Summary: In this paper, a new class of positively p-nuclear operators is introduced and investigated, which are positive analogues of right p-nuclear operators. One of the main results establishes the identification between the dual space of positively p-nuclear operators and the class of positive p-majorizing operators, which is a dual notion of positive p-summing operators. The paper also presents the duality relationships between lattically p-nuclear operators and positively p-nuclear operators, and introduces the concept of positively p-integral operators via positively p-nuclear operators. The space of positively p-integral operators is described as the dual of a closure of finite rank operators in the space of positive p-majorizing operators.

POSITIVITY (2022)

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Prime ideals and Noetherian properties in vector lattices

Marko Kandic et al.

Summary: In this paper, we investigate the set of prime ideals in vector lattices and how the properties of the prime ideals structure the vector lattice under consideration. The different properties that will be explored include the order density of prime ideals, the finiteness of prime ideals, the primality of every prime ideal, and the stationarity of every ascending chain of prime ideals (referred to as prime Noetherian property). We also provide a complete characterization of prime ideals in vector lattices of piecewise polynomials, which proves to be an interesting class for studying principal prime ideals and ascending chains of prime ideals.

POSITIVITY (2022)

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Article Mathematics