TY - JOUR AU - Tarcsay, Zsigmond AU - Sebestyén, Zoltán TI - Reduction of positive self-adjoint extensions JF - OPUSCULA MATHEMATICA J2 - OPUSC MATHEMATICA VL - 44 PY - 2024 IS - 3 SP - 425 EP - 438 PG - 14 SN - 1232-9274 DO - 10.7494/OpMath.2024.44.3.425 UR - https://m2.mtmt.hu/api/publication/34751048 ID - 34751048 N1 - Zsigmond Tarcsay was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP–22-5-ELTE-1096 New National Excellence Program of the Ministry for Innovation and Technology. LA - English DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond AU - Göde, Ábel TI - Operators on anti-dual pairs. Supremum and infimum of positive operators TS - Supremum and infimum of positive operators JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 531 PY - 2024 IS - Issue 2, Part 2 PG - 11 SN - 0022-247X DO - 10.1016/j.jmaa.2023.127893 UR - https://m2.mtmt.hu/api/publication/34317106 ID - 34317106 N1 - Zs. Tarcsay was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP–22-5-ELTE-1096 New National Excellence Program of the Ministry for Innovation and Technology LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - Extensions of positive symmetric operators and Krein's uniqueness criteria JF - LINEAR AND MULTILINEAR ALGEBRA J2 - LINEAR MULTILINEAR A PY - 2023 SN - 0308-1087 DO - 10.1080/03081087.2023.2196610 UR - https://m2.mtmt.hu/api/publication/33766588 ID - 33766588 N1 - Export Date: 11 September 2023 Correspondence Address: Tarcsay, Z.; Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c, Hungary; email: zsigmond.tarcsay@ttk.elte.hu LA - English DB - MTMT ER - TY - CONF AU - Tarcsay, Zsigmond TI - Pozitív operátorok struktúrái T2 - Intézményi ÚNKP Konferencia 2022 PB - Eötvös Loránd Tudományegyetem (ELTE) C1 - Budapest PY - 2022 SP - 325 UR - https://m2.mtmt.hu/api/publication/33126635 ID - 33126635 LA - Hungarian DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond TI - Maps preserving the Douglas solution of operator equations JF - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS J2 - J MATH ANAL APPL VL - 507 PY - 2022 IS - 2 SN - 0022-247X DO - 10.1016/j.jmaa.2021.125802 UR - https://m2.mtmt.hu/api/publication/32508425 ID - 32508425 N1 - Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/c., Budapest, H-1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15., Budapest, H-1053, Hungary Export Date: 17 October 2022 Correspondence Address: Tarcsay, Z.; Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c., Hungary; email: zsigmond.tarcsay@ttk.elte.hu LA - English DB - MTMT ER - TY - JOUR AU - Horváth, Bence AU - Tarcsay, Zsigmond TI - Perturbations of surjective homomorphisms between algebras of operators on Banach spaces JF - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY J2 - P AM MATH SOC VL - 150 PY - 2022 IS - 2 SP - 747 EP - 761 PG - 15 SN - 0002-9939 DO - 10.1090/proc/15666 UR - https://m2.mtmt.hu/api/publication/32080872 ID - 32080872 N1 - Institute of Mathematics, Czech Academy of Sciences, Žitná 25, Prague 1, 115 67, Czech Republic Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, Budapest, H-1053, Hungary Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/c, Budapest, H-1117, Hungary Cited By :1 Export Date: 21 February 2023 Funding details: 308015 Funding details: TKP2020-NKA-06 Funding details: Magyar Tudományos Akadémia, MTA Funding details: Innovációs és Technológiai Minisztérium Funding text 1: The second author was supported by DAAD-TEMPUS Cooperation Project “Harmonic Analysis and Extremal Problems” (grant no. 308015), by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the ÚNKP–20-5-ELTE-185 New National Excellence Program of the Ministry for Innovation and Technology. “Application Domain Specific Highly Reliable IT Solutions” project has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, financed under the Thematic Excellence Programme TKP2020-NKA-06 (National Challenges Subprogramme) funding scheme. LA - English DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond AU - Titkos, Tamás TI - Operators on anti-dual pairs: Generalized Krein-von Neumann extension JF - MATHEMATISCHE NACHRICHTEN J2 - MATH NACHR VL - 294 PY - 2021 IS - 9 SP - 1821 EP - 1838 PG - 18 SN - 0025-584X DO - 10.1002/mana.201800431 UR - https://m2.mtmt.hu/api/publication/32163878 ID - 32163878 N1 - Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Pázmány Péter sétány 1/c., Budapest, H-1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, Budapest, H-1053, Hungary BBS University of Applied Sciences, Alkotmány u. 9, Budapest, H-1054, Hungary Export Date: 4 July 2022 Correspondence Address: Tarcsay, Z.; Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c., Hungary; email: tarcsay@cs.elte.hu AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Sebestyén, Zoltán AU - Tarcsay, Zsigmond TI - On the Krein-von Neumann and Friedrichs extension of positive operators JF - ACTA WASAENSIA J2 - ACTA WASA VL - 462 PY - 2021 SP - 165 EP - 178 PG - 14 SN - 0355-2667 UR - https://m2.mtmt.hu/api/publication/32080890 ID - 32080890 LA - English DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond AU - Sebestyén, Zoltán TI - Canonical Graph Contractions of Linear Relations on Hilbert Spaces JF - COMPLEX ANALYSIS AND OPERATOR THEORY J2 - COMPLEX ANAL OPER TH VL - 15 PY - 2021 IS - 1 SN - 1661-8254 DO - 10.1007/s11785-020-01066-3 UR - https://m2.mtmt.hu/api/publication/31840162 ID - 31840162 N1 - Export Date: 7 September 2022 Correspondence Address: Tarcsay, Z.; Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/c, Hungary; email: tarcsay@cs.elte.hu LA - English DB - MTMT ER - TY - JOUR AU - Tarcsay, Zsigmond AU - Titkos, Tamás TI - Operators on anti-dual pairs: Generalized Schur complement JF - LINEAR ALGEBRA AND ITS APPLICATIONS J2 - LINEAR ALGEBRA APPL VL - 614 PY - 2021 SP - 125 EP - 143 PG - 19 SN - 0024-3795 DO - 10.1016/j.laa.2020.02.031 UR - https://m2.mtmt.hu/api/publication/31203615 ID - 31203615 N1 - Közlésre elfogadva: 25-Feb-2020 Online megjelenés: 28-February-2020 AB - 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. LA - English DB - MTMT ER -