Isometries on positive operators of unit norm

Nagy, Gergő

doi:10.5486/pmd.2013.5396

Cited by 17 publications

(18 citation statements)

References 8 publications

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“…However, if we assume the preservation of the norm of only a fixed linear combination, then the description of the structure of the corresponding transformations may become much more difficult. As for this problem, in [3] the author proved two results related to the general form of the isometries of ( ) + 1 . Motivated mainly by the theorems in [2,3], in this paper, we present several statements concerning the structure of those maps on ( ) + or on ( ) + 1 which preserve the norm of linear combinations with fixed real coefficients.…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Preservers for thep-Norm of Linear Combinations of Positive Operators

Nagy

2014

Abstract and Applied Analysis

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Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Preservers for thep-Norm of Linear Combinations of Positive Operators

Nagy

2014

Abstract and Applied Analysis

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“…However, as a consequence of the result ∆ is surjective. Theorem 6.3 was extended by G. Nagy to arbitrary complex Hilbert spaces in [36]. Theorem 6.4.…”

Section: Isometries Between the Spheres Of Positive Operatorsmentioning

confidence: 99%

A survey on Tingley’s problem for operator algebras

Peralta¹

2018

Acta Sci. Math.

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We survey the most recent results on extension of isometries between special subsets of the unit spheres of C * -algebras, von Neumann algebras, trace class operators, preduals of von Neumann algebras, and p-Schattenvon Neumann spaces, with special interest on Tingley's problem.Problem 1.1. Let X and Y be two Banach spaces whose unit spheres are denoted by S(X) and S(Y ), respectively. Let S 1 and S 2 be two subsets of S(X) and S(Y ), respectively. Suppose ∆ : S 1 → S 2 is a surjective isometry. Does ∆ extend to a real linear isometry from X onto Y ?Henceforth, we shall write T for the unit sphere of C. The complex conjugation on T cannot be extended to a complex linear isometry on C. So, in the case of complex Banach spaces, a complex linear extension is simply hopeless for all cases. Similar constrains will appear in subsequent results.These problems, whose origins are in geometry, are nowadays a central topic for those researchers working on preservers. If in Problem 1.1 we consider S 1 = S(X) and S 2

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“…The Danube runs 417-km long in Hungary, which gives tasks to many settlements during flood protection (NAGY, 2013). However, protection is not only the responsibility of the municipalities.…”

Section: Danube Flood (2013)mentioning

confidence: 99%

The role and importance of environmental administration in the protection against environmental damages

László¹

2020

VSS

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In this study, the author presents the central, regional and local levels of environmental administration in Hungary and their tasks. Through two specific examples (the Danube Flood and the 2010 Kolontár Red Sludge Disaster), she analyzes the incidents damaging the environment, their consequences and impacts. She also proves that the cooperation between municipalities and regional environmental and disaster management bodies is inevitable. She studies the role played by the environmental administration in the protection and makes suggestions for improving the efficiency of protection. In the context of the two incidents, she analyzes the possibilities of the environmental administration in the protection against environmental damages and makes recommendations on its development.

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Isometries on positive operators of unit norm

Abstract: Abstract. Let p > 1 be a real number. We describe the structure of surjective isometries of the space of all positive operators in the unit sphere of the von Neumann-Schatten p-class. In the finite dimensional case we extend the obtained result for 'a priori' nonsurjective transformations.

Cited by 17 publications

References 8 publications

Preservers for thep-Norm of Linear Combinations of Positive Operators

Preservers for thep-Norm of Linear Combinations of Positive Operators

A survey on Tingley’s problem for operator algebras

The role and importance of environmental administration in the protection against environmental damages

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