scholarly journals Order among power operator means with condition on spectra

2011 ◽  
pp. 709-716
Author(s):  
Jadranka Mić ć Hot ◽  
Zlatko Pavić ◽  
Josip Pečarić
Keyword(s):  
Operator Means

GEODESICS AND OPERATOR MEANS IN THE SPACE OF POSITIVE OPERATORS

1993 ◽  
Vol 04 (02) ◽  
pp. 193-202 ◽  
Author(s):  
GUSTAVO CORACH ◽  
HORACIO PORTA ◽  
LÁZARO RECHT
Keyword(s):  
Geometric Mean ◽  
Geodesic Segment ◽  
Finsler Metric ◽  
Natural Structure ◽  
Operator Inequalities ◽  
C Algebra ◽  
Operator Means ◽  
Natural Notion ◽  
Invertible Elements ◽  
Classical Convexity

The set A+ of positive invertible elements of a C*-algebra has a natural structure of reductive homogeneous manifold with a Finsler metric. Because pairs of points can be joined by uniquely determined geodesics and geodesics are "short" curves, there is a natural notion of convexity: C ⊂ A+ is convex if the geodesic segment joining a, b ∈ C is contained in C. We show that this notion is related to the classical convexity of real and operator valued functions. Several results about convexity are proved in this paper. The expressions of these results are closely related to the operator means of Kubo and Ando, in particular to the geometric mean of Pusz and Woronowicz, and they produce several norm estimations and operator inequalities.

scholarly journals A new class of operator monotone functions via operator means

2016 ◽  
Vol 64 (12) ◽  
pp. 2463-2473 ◽  
Author(s):  
Rajinder Pal ◽  
Mandeep Singh ◽  
Mohammad Sal Moslehian ◽  
Jaspal Singh Aujla
Keyword(s):  
Monotone Functions ◽  
New Class ◽  
Operator Monotone ◽  
Operator Means ◽  
Operator Monotone Functions

Some operator inequalities involving operator means and positive linear maps

2017 ◽  
Vol 66 (6) ◽  
pp. 1186-1198 ◽  
Author(s):  
Maryam Khosravi ◽  
Mohammad Sal Moslehian ◽  
Alemeh Sheikhhosseini
Keyword(s):  
Operator Inequalities ◽  
Linear Maps ◽  
Operator Means ◽  
Positive Linear Maps

scholarly journals A new quantum operator for distance

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950033
Author(s):  
Daniel Katz
Keyword(s):  
Quantum Mechanics ◽  
Equivalence Principle ◽  
Classical Mechanics ◽  
Proof Of Concept ◽  
Logical Relationship ◽  
Weak Equivalence Principle ◽  
Quantum Operator ◽  
Operator Means ◽  
Definition Of ◽  
Future Work

We introduce a new semirelativistic quantum operator for the length of the worldline a particle traces out as it moves. In this article the operator is constructed in a heuristic way and some of its elementary properties are explored. The operator ends up depending in a very complicated way on the potential of the system it is to act on so as a proof of concept we use it to analyze the expected distance traveled by a free Gaussian wave packet with some initial momentum. It is shown in this case that the distance such a particle travels becomes light-like as its mass vanishes and agrees with the classical result for macroscopic masses. This preliminary result has minor implications for the Weak Equivalence Principle (WEP) in quantum mechanics. In particular it shows that the logical relationship between two formulations of the WEP in classical mechanics extends to quantum mechanics. That our result is qualitatively consistent with the work of others emboldens us to start the task of evaluating the new operator in nonzero potentials. However, we readily acknowledge that the looseness in the definition of our operator means that all of our so-called results are highly speculative. Plans for future work with the new operator are discussed in the last section.

scholarly journals Ando–Hiai-type inequalities for operator means and operator perspectives

2019 ◽  
Vol 31 (01) ◽  
pp. 2050007
Author(s):  
Fumio Hiai ◽  
Yuki Seo ◽  
Shuhei Wada
Keyword(s):  
Positive Operators ◽  
Extension Problem ◽  
Operator Means ◽  
Trotter Formula

We improve the existing Ando–Hiai inequalities for operator means and present new ones for operator perspectives in several ways. We also provide the operator perspective version of the Lie–Trotter formula and consider the extension problem of operator perspectives to non-invertible positive operators.

Operator means and matrix quadratic equations

2021 ◽  
Vol 609 ◽  
pp. 163-175
Author(s):  
Mitsuru Uchiyama
Keyword(s):  
Quadratic Equations ◽  
Operator Means

scholarly journals A converse of Loewner–Heinz inequality and applications to operator means

2014 ◽  
Vol 413 (1) ◽  
pp. 422-429 ◽  
Author(s):  
Mitsuru Uchiyama ◽  
Takeaki Yamazaki
Keyword(s):  
Heinz Inequality ◽  
Operator Means

scholarly journals TOTAL LOGIC

2014 ◽  
Vol 7 (3) ◽  
pp. 529-547 ◽  
Author(s):  
STEPHAN LEUENBERGER
Keyword(s):  
Model Theory ◽  
Propositional Logic ◽  
Fundamental Nature ◽  
The World ◽  
Operator Means ◽  
Negative Truths

AbstractA typical first stab at explicating the thesis of physicalism is this: physicalism is true iff every fact about the world is entailed by the conjunction of physical facts. The same holds, mutatis mutandis, for other hypotheses about the fundamental nature of our world. But it has been recognized that this would leave such hypotheses without the fighting chance that they deserve: certain negative truths, like the truth (if it is one) that there are no angels, are not entailed by the physical facts, but nonetheless do not threaten physicalism. A plausible remedy that has been suggested by Jackson and Chalmers is that physicalism boils down to the thesis that every truth is entailed by the conjunction of the physical facts prefixed by a “that’s it” or “totality” operator. To evaluate this suggestion, we need to know what that operator means, and—since the truth of physicalism hinges on what is entailed by a totality claim—what its logic is. That is, we need to understand the logic of totality, or total logic. In this paper, I add a totality operator to the language of propositional logic and present a model theory for it, building on a suggestion by Chalmers and Jackson. I then prove determination results for a number of different systems.

Operator means and networks

1991 ◽  
Vol 14 (2) ◽  
pp. 157-182
Author(s):  
Jonathan Arazy
Keyword(s):  
Operator Means
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