Space pre-order and minus partial order for operators on Banach spaces

DOI10.1007/s00010-012-0133-2zbMath1275.47006OpenAlexW1984700097MaRDI QIDQ2375917

Dragan S. Rakić, Dragan S. Djordjević

Publication date: 25 June 2013

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-012-0133-2

zbMATH Keywords

generalized inversesminus partial orderoperator matricesspace pre-order

Mathematics Subject Classification ID

Partial orders, general (06A06) Theory of matrix inversion and generalized inverses (15A09) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05)

Related Items (15)

Core inverse and core partial order of Hilbert space operators ⋮ Weighted binary relations for operators on Banach spaces ⋮ Partial orders based on inverses along elements ⋮ Further properties on the core partial order and other matrix partial orders ⋮ On partial orders of operators ⋮ Weighted G-Drazin inverses and a new pre-order on rectangular matrices ⋮ GD1 inverse and 1GD inverse for bounded operators on Banach spaces ⋮ 1MP and MP1 inverses and one-sided star orders in a ring with involution ⋮ Moore-Penrose inverse and partial orders on Hilbert space operators ⋮ On some new pre-orders defined by weighted Drazin inverses ⋮ Some orders for operators on Hilbert spaces ⋮ Minus partial order and linear preservers ⋮ New matrix partial order based on spectrally orthogonal matrix decomposition ⋮ Bimonotone maps on semiprime Banach algebras ⋮ Partial orders on \(\mathcal{B}(\mathcal{H})\)

Cites Work

• Invertibility of a linear combination of two matrices and partial orderings
• Solving a minus partial ordering equation over von Neumann regular rings.
• Matrix partial orders through generalized inverses: Unified theory
• Automorphisms of \(B(H)\) with respect to minus partial order
• On parallel summability of matrices
• Shorted operators and rank decomposition matrices
• On some characterizations of the star partial ordering for matrices and rank subtractivity
• A relationship between the star and minus orderings
• The minus partial order and the shorted matrix
• Infimum of a pair of matrices
• On the Löwner, minus, and star partial orderings of nonnegative definite matrices and their squares
• A note on the rank-subtractivity ordering
• Nonnegative idempotent matrices and the minus partial order
• The maximal and minimal ranks of \(A - BXC\) with applications
• Some properties of matrix partial orderings
• Automorphisms of \(M_{n}\), partially ordered by rank subtractivity ordering
• Shorted Operators Relative to a Partial Order in a Regular Ring
• A Natural Partial Order for Semigroups
• Majorization, range inclusion, and factorization for bounded linear operators
• On Majorization, Factorization, and Range Inclusion of Operators on Hilbert Space
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