@article{MTMT:3056013, title = {LEBESGUE DECOMPOSITION FOR REPRESENTABLE FUNCTIONALS ON *-ALGEBRAS}, url = {https://m2.mtmt.hu/api/publication/3056013}, author = {Tarcsay, Zsigmond}, doi = {10.1017/S0017089515000300}, journal-iso = {GLASGOW MATH J}, journal = {GLASGOW MATHEMATICAL JOURNAL}, volume = {58}, unique-id = {3056013}, issn = {0017-0895}, abstract = {We offer a Lebesgue-type decomposition of a representable functional on a *-algebra into absolutely continuous and singular parts with respect to another. Such a result was proved by Zs. Szűcs due to a general Lebesgue decomposition theorem of S. Hassi, H.S.V. de Snoo, and Z. Sebestyén concerning non-negative Hermitian forms. In this paper, we provide a self-contained proof of Szűcs' result and in addition we prove that the corresponding absolutely continuous parts are absolutely continuous with respect to each other. Copyright © Glasgow Mathematical Journal Trust 2015}, year = {2016}, eissn = {1469-509X}, pages = {491-501}, orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055} } @article{MTMT:2937121, title = {On the parallel sum of positive operators, forms, and functionals}, url = {https://m2.mtmt.hu/api/publication/2937121}, author = {Tarcsay, Zsigmond}, doi = {10.1007/s10474-015-0533-6}, journal-iso = {ACTA MATH HUNG}, journal = {ACTA MATHEMATICA HUNGARICA}, volume = {147}, unique-id = {2937121}, issn = {0236-5294}, abstract = {The parallel sum (Formula presented.) of two bounded positive linear operators A, B on a Hilbert space H is defined to be the positive operator having the quadratic form(Formula presented.)for fixed (Formula presented.). The purpose of this paper is to provide a factorization of the parallel sum of the form (Formula presented.) where (Formula presented.) is the embedding operator of an auxiliary Hilbert space associated with A and B, and P is an orthogonal projection onto a certain linear subspace of that Hilbert space. We give similar factorizations of the parallel sum of nonnegative Hermitian forms, positive operators of a complex Banach space E into its topological anti-dual (Formula presented.), and of representable positive functionals on a (Formula presented.)-algebra. © 2015 Akadémiai Kiadó, Budapest, Hungary}, year = {2015}, eissn = {1588-2632}, pages = {408-426}, orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055} } @article{MTMT:2532851, title = {Lebesgue decomposition theorems}, url = {https://m2.mtmt.hu/api/publication/2532851}, author = {Sebestyén, Zoltán and Tarcsay, Zsigmond and Titkos, Tamás}, journal-iso = {ACTA SCI MATH (SZEGED)}, journal = {ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)}, volume = {79}, unique-id = {2532851}, issn = {0001-6969}, keywords = {Singularity; Lebesgue decomposition; Nonnegative forms; Absolute continuity; Hilbert space methods}, year = {2013}, pages = {219-233}, orcid-numbers = {Tarcsay, Zsigmond/0000-0001-8102-5055} } @article{MTMT:2406323, title = {Lebesgue type decompositions for nonnegative forms}, url = {https://m2.mtmt.hu/api/publication/2406323}, author = {Hassi, S and Sebestyén, Zoltán and de Snoo, H}, doi = {10.1016/j.jfa.2009.09.014}, journal-iso = {J FUNCT ANAL}, journal = {JOURNAL OF FUNCTIONAL ANALYSIS}, volume = {257}, unique-id = {2406323}, issn = {0022-1236}, year = {2009}, eissn = {1096-0783}, pages = {3858-3894} }