@article{MTMT:33720234,
	title = {On the exotic isometry flow of the quadratic Wasserstein space over the real line},
	url = {https://m2.mtmt.hu/api/publication/33720234},
	author = {Gehér, G.P. and Titkos, Tamás and Virosztek, Dániel},
	doi = {10.1016/j.laa.2023.02.016},
	journal-iso = {LINEAR ALGEBRA APPL},
	journal = {LINEAR ALGEBRA AND ITS APPLICATIONS},
	volume = {Available online 6 March 2023},
	unique-id = {33720234},
	issn = {0024-3795},
	abstract = {Kloeckner discovered that the quadratic Wasserstein space over the real line (denoted by W2(R)) is quite peculiar, as its isometry group contains an exotic isometry flow. His result implies that it can happen that an isometry Φ fixes all Dirac measures, but still, Φ is not the identity of W2(R). This is the only known example of this surprising and counterintuitive phenomenon. Kloeckner also proved that the image of each finitely supported measure under these isometries (and thus under all isometry) is a finitely supported measure. Recently we showed that the exotic isometry flow can be represented as a unitary group on L2((0,1)). In this paper, we calculate the generator of this group, and we show that every exotic isometry (and thus every isometry) maps the set of all absolutely continuous measures belonging to W2(R) onto itself. © 2023 Elsevier Inc.},
	keywords = {Unitary group; Real line; Isometric embeddings; Isometric embeddings; Wasserstein space; Counter-intuitive phenomenon; isometric rigidity; isometric rigidity; Exotic isometry flow; Exotic isometry flow; Dirac measures; Wasserstein spaces},
	year = {2024},
	eissn = {1873-1856},
	pages = {&}
}

@misc{MTMT:34131047,
	title = {Isometric rigidity of Wasserstein spaces over Euclidean spheres},
	url = {https://m2.mtmt.hu/api/publication/34131047},
	author = {Gehér, György and Hruskova, Aranka and Titkos, Tamás and Virosztek, Dániel},
	unique-id = {34131047},
	year = {2023},
	orcid-numbers = {Gehér, György/0000-0003-1499-3229}
}

@article{MTMT:33678624,
	title = {On isometries of Wasserstein spaces},
	url = {https://m2.mtmt.hu/api/publication/33678624},
	author = {Gehér, György and Titkos, Tamás and Virosztek, Dániel},
	journal-iso = {RIMS KOKYUROKU BESSATSU},
	journal = {RIMS KOKYUROKU BESSATSU},
	volume = {B93},
	unique-id = {33678624},
	issn = {1881-6193},
	year = {2023},
	pages = {239-250},
	orcid-numbers = {Gehér, György/0000-0003-1499-3229}
}

@article{MTMT:33578758,
	title = {Isometric rigidity of Wasserstein tori and spheres},
	url = {https://m2.mtmt.hu/api/publication/33578758},
	author = {Gehér, György and Titkos, Tamás and Virosztek, Dániel},
	doi = {10.1112/mtk.12174},
	journal-iso = {MATHEMATIKA},
	journal = {MATHEMATIKA},
	volume = {69},
	unique-id = {33578758},
	issn = {0025-5793},
	abstract = {We prove isometric rigidity for p-Wasserstein spaces over finite-dimensional tori and spheres for all p. We present a unified approach to proving rigidity that relies on the robust method of recovering measures from their Wasserstein potentials. © 2022 The Authors. The publishing rights in this article are licensed to University College London under an exclusive licence. Mathematika is published by the London Mathematical Society on behalf of University College London.},
	year = {2023},
	eissn = {2041-7942},
	pages = {20-32},
	orcid-numbers = {Gehér, György/0000-0003-1499-3229}
}

@article{MTMT:33578756,
	title = {Quantum Wasserstein isometries on the qubit state space},
	url = {https://m2.mtmt.hu/api/publication/33578756},
	author = {Gehér, György and Pitrik, József and Titkos, Tamás and Virosztek, Dániel},
	doi = {10.1016/j.jmaa.2022.126955},
	journal-iso = {J MATH ANAL APPL},
	journal = {JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS},
	volume = {522},
	unique-id = {33578756},
	issn = {0022-247X},
	abstract = {We describe Wasserstein isometries of the quantum bit state space with respect to distinguished cost operators. We derive a Wigner-type result for the cost operator involving all the Pauli matrices: in this case, the isometry group consists of unitary or anti-unitary conjugations. In the Bloch sphere model this means that the isometry group coincides with the classical symmetry group O(3). On the other hand, for the cost generated by the qubit ‘‘clock” and ‘‘shift” operators, we discovered non-surjective and non-injective isometries as well, beyond the regular ones. This phenomenon mirrors certain surprising properties of the quantum Wasserstein distance. © 2022 Elsevier Inc.},
	keywords = {isometries; Quantum bits; Quantum optimal transport},
	year = {2023},
	eissn = {1096-0813},
	orcid-numbers = {Gehér, György/0000-0003-1499-3229}
}

@article{MTMT:33578940,
	title = {A Tingley-sejtés},
	url = {https://m2.mtmt.hu/api/publication/33578940},
	author = {Titkos, Tamás},
	journal-iso = {ÉRINTŐ},
	journal = {ÉRINTŐ : ELEKTRONIKUS MATEMATIKAI LAPOK},
	unique-id = {33578940},
	year = {2022},
	eissn = {2559-9275}
}

@article{MTMT:33195355,
	title = {ISOMETRIC RIGIDITY OF WASSERSTEIN SPACES: THE GRAPH METRIC CASE},
	url = {https://m2.mtmt.hu/api/publication/33195355},
	author = {Kiss, Gergely and Titkos, Tamás},
	doi = {10.1090/proc/15977},
	journal-iso = {P AM MATH SOC},
	journal = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
	volume = {150},
	unique-id = {33195355},
	issn = {0002-9939},
	abstract = {The aim of this paper is to prove that the p-Wasserstein space Wp(X) is isometrically rigid for all p ≥ 1 whenever X is a countable graph metric space. As a consequence, we obtain that for every countable group H and any p ≥ 1 there exists a p-Wasserstein space whose isometry group is isomorphic to H. © 2022 American Mathematical Society},
	keywords = {Isometry; Wasserstein space; graph metric space; isometric rigidity},
	year = {2022},
	eissn = {1088-6826},
	pages = {4083-4097}
}

@article{MTMT:31855431,
	title = {The isometry group of Wasserstein spaces: the Hilbertian case},
	url = {https://m2.mtmt.hu/api/publication/31855431},
	author = {Gehér, György and Titkos, Tamás and Virosztek, Dániel},
	doi = {10.1112/jlms.12676},
	journal-iso = {J LOND MATH SOC},
	journal = {JOURNAL OF THE LONDON MATHEMATICAL SOCIETY},
	volume = {106},
	unique-id = {31855431},
	issn = {0024-6107},
	abstract = {Motivated by Kloeckner's result on the isometry group of the quadratic Wasserstein space (Formula presented.), we describe the isometry group (Formula presented.) for all parameters (Formula presented.) and for all separable real Hilbert spaces (Formula presented.). In particular, we show that (Formula presented.) is isometrically rigid for all Polish space (Formula presented.) whenever (Formula presented.). This is a consequence of our more general result: we prove that (Formula presented.) is isometrically rigid if (Formula presented.) is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters (Formula presented.), by solving Kloeckner's problem affirmatively on the existence of mass-splitting isometries. As a byproduct of our methods, we also obtain the isometric rigidity of (Formula presented.) for all complete and separable ultrametric spaces (Formula presented.) and parameters (Formula presented.). © 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.},
	year = {2022},
	eissn = {1469-7750},
	pages = {3836-3894},
	orcid-numbers = {Gehér, György/0000-0003-1499-3229}
}

@article{MTMT:32163878,
	title = {Operators on anti-dual pairs: Generalized Krein-von Neumann extension},
	url = {https://m2.mtmt.hu/api/publication/32163878},
	author = {Tarcsay, Zsigmond and Titkos, Tamás},
	doi = {10.1002/mana.201800431},
	journal-iso = {MATH NACHR},
	journal = {MATHEMATISCHE NACHRICHTEN},
	volume = {294},
	unique-id = {32163878},
	issn = {0025-584X},
	abstract = {The main aim of this paper is to generalize the classical concept of a positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The concept of anti-duality carries an adequate structure to define positivity in a natural way, and is still general enough to cover numerous important areas where the Hilbert space theory cannot be applied. Our running example - illustrating the applicability of the general setting to spaces bearing poor geometrical features - comes from noncommutative integration theory. Namely, representable extension of linear functionals of involutive algebras will be governed by their induced operators. The main theorem, to which the vast majority of the results is built, gives a complete and constructive characterization of those operators that admit a continuous positive extension to the whole space. Various properties such as commutation, or minimality and maximality of special extensions will be studied in detail.},
	keywords = {Kernel; Positive operator; operator extension; *-algebra; positive functional; anti-duality},
	year = {2021},
	eissn = {1522-2616},
	pages = {1821-1838},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055}
}

@article{MTMT:31203615,
	title = {Operators on anti-dual pairs: Generalized Schur complement},
	url = {https://m2.mtmt.hu/api/publication/31203615},
	author = {Tarcsay, Zsigmond and Titkos, Tamás},
	doi = {10.1016/j.laa.2020.02.031},
	journal-iso = {LINEAR ALGEBRA APPL},
	journal = {LINEAR ALGEBRA AND ITS APPLICATIONS},
	volume = {614},
	unique-id = {31203615},
	issn = {0024-3795},
	abstract = {The goal of this paper is to develop the theory of Schur complementation in the context of operators acting on anti-dual pairs. As a byproduct, we obtain a natural generalization of the parallel sum and parallel difference, as well as the Lebesgue-type decomposition. To demonstrate how this operator approach works in application, we derive the corresponding results for operators acting on rigged Hilbert spaces, and for representable functionals of ⁎-algebras.},
	year = {2021},
	eissn = {1873-1856},
	pages = {125-143},
	orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055; Titkos, Tamás/0000-0002-3891-7020}
}