Journal ArticleDOI
Inequalities for the hadamard weighted geometric mean of positive kernel operators on banach function spaces
Roman Drnovšek,Aljoša Peperko +1 more
TLDR
In this article, the Hadamard weighted geometric mean of K1,..., Kn, the operator K, satisfies the following inequalities for positive kernel operators on a Banach function space.Abstract:
Let K1, . . . , Kn be positive kernel operators on a Banach function space. We prove that the Hadamard weighted geometric mean of K1, . . . , Kn, the operator K, satisfies the following inequalitiesread more
Citations
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Journal ArticleDOI
Inequalities for the spectral radius of non-negative functions
TL;DR: In this article, the spectral radius rh (f) of f ∈ M(X × X)+ with respect to h and * has been introduced, which provides a generalization and unification of a non-negative matrix.
Journal ArticleDOI
On the max version of the generalized spectral radius theorem
TL;DR: In this article, the max algebra version of the generalized spectral radius of nonnegative matrices was introduced, and a short proof of the max version of GSR theorem was given.
Journal ArticleDOI
Bounds on the generalized and the joint spectral radius of Hadamard products of bounded sets of positive operators on sequence spaces
TL;DR: In this paper, the generalized and joint spectral radius of bounded sets of operators on sequence spaces was shown to be bounded by ρ (A ∘ B ) ≤ ρ 1 2 ( ( A ∘ A ) (B ∘B ) ) ≤ ∆ ( AB ∘ AB ) 1 4 ρ( BA ∘ BA ).
Journal ArticleDOI
Bounds on the spectral radius of Hadamard products of positive operators on lp-spaces
TL;DR: In this article, Audenaert et al. proved inequalities between the spectral radius of Hadamard products of finite nonnegative matrices and their ordinary matrix product, and extended these inequalities in such a way that they extend to infinite nonnegative matrix A and B that define bounded operators on the classical sequence spaces.
Journal ArticleDOI
On the spectral radius of positive operators on Banach sequence spaces
Roman Drnovšek,Aljoša Peperko +1 more
TL;DR: In this article, the spectral radius is shown to be a convex function of the diagonal entries of a non-negative matrix and the largest function f for which this inequality holds for all K 1, …, K n.
References
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Book
Positive Operators
TL;DR: Book of positive operators, as an amazing reference becomes what you need to get, and book, as a source that may involve the facts, opinion, literature, religion, and many others are the great friends to join with.
Book
Riesz Spaces, II
TL;DR: In this paper, the authors present a survey of L p Spaces and Compact Operators, including Orthomorphisms and f-Algebras, as well as Kernel Operators.
Journal ArticleDOI
The perron root of a weighted geometric mean of nonneagative matrices
TL;DR: For k nonnegative n-by-n matrices A 1, A k, where A k is the matrix where is the (entry-wise) Hadamard product and is the component-wise weighted geometric mean of it is shown that for the inequality holds.
Journal ArticleDOI
Tight bounds on the spectral radius of asymmetric nonnegative matrices
TL;DR: In this article, the authors identify a pair of symmetric matrices whose largest eigenvalues bound the spectral radius of an arbitrary asymmetric nonnegative n × n matrix A and show that these bounding matrices are best characterized by characterizing matrices A which attain equality with either the upper or lower bounding matrix.