a ) p. 131 The discussion between eqs. (5.14) and (5.15) is incorrect (dA should be made as large as possible!). b ) p. 256 In the figure, the numbers 6) and 7) occur twice. c ) p. 292 At the end of section 12.5, it should be the space of isospectral 0Hermitian matrices. d ) p. 306 A ”Tr” is missing in eq. (13.43). e ) p. 327, Eq. (14.64b) is 〈Trρ〉B = N(14N+10) (5N+1)(N+3) should be 〈Trρ〉B = 8N+7 (N+2)(N+4)

Geometry of Quantum States: Frontmatter

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A Course In Functional Analysis

https://chaos.if.uj.edu.pl/~karol/erratum10.pdf

Geometry of Quantum States

We present a comprehensive and up-to-date review of the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of a quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.

https://iopscience.iop.org/article/10.1088/0034-4885/77/9/094001/pdf

Quantum non-Markovianity: characterization, quantification and detection

Geometry of quantum states: an introduction to quantum entanglement by Ingemar Bengtsson and Karol Zyczkowski

Some Linear and Multiplicative Preserver Problems on Operator Algebras and Function Algebras.- Preservers on Quantum Structures.- Local Automorphisms and Local Isometries of Operator Algebras and Function Algebras.

/pdf/selected-preserver-problems-on-algebraic-structures-of-4w2wh1orzi.pdf

Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces

We present some nonlinear characterizations of the automorphisms of the operator algebra $B(H)$ and the function algebra $C(X)$ by means of their spectrum preserving properties.

Some characterizations of the automorphisms of $B(H)$ and $C(X)$

We present some nonlinear characterizations of the automorphisms of the operator algebra B(H) and the function algebra C(X) by means of their spectrum preserving properties

/pdf/some-characterizations-of-the-automorphisms-of-b-h-and-c-x-3lpindvf8y.pdf

Some characterizations of the automorphisms of B(H) and C(X)

Orthogonality Preserving Transformations on Indefinite Inner Product Spaces: Generalization of Uhlhorn's Version of Wigner's Theorem

We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents of a Banach space which preserve zero products in both directions.

Lajos Molnár

Papers

Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces

Some characterizations of the automorphisms of $B(H)$ and $C(X)$

Some characterizations of the automorphisms of B(H) and C(X)

Orthogonality Preserving Transformations on Indefinite Inner Product Spaces: Generalization of Uhlhorn's Version of Wigner's Theorem

Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem