Open Access
April 2017 Lattice properties of the core-partial order
Marko S. Djikić
Banach J. Math. Anal. 11(2): 398-415 (April 2017). DOI: 10.1215/17358787-0000010X


We show that in an arbitrary Hilbert space, the set of group-invertible operators with respect to the core-partial order has the complete lower semilattice structure, meaning that an arbitrary family of operators possesses the core-infimum. We also give a necessary and sufficient condition for the existence of the core-supremum of an arbitrary family, and we study the properties of these lattice operations on pairs of operators.


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Marko S. Djikić. "Lattice properties of the core-partial order." Banach J. Math. Anal. 11 (2) 398 - 415, April 2017.


Received: 12 March 2016; Accepted: 29 June 2016; Published: April 2017
First available in Project Euclid: 7 March 2017

zbMATH: 06694361
MathSciNet: MR3620129
Digital Object Identifier: 10.1215/17358787-0000010X

Primary: 47A05
Secondary: ‎15A09 , 46C05

Keywords: core-infimum , core-parallel , core-partial order , core-supremum

Rights: Copyright © 2017 Tusi Mathematical Research Group

Vol.11 • No. 2 • April 2017
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