@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:2569368, title = {On Means of Nonnegative Sesquilinear Forms}, url = {https://m2.mtmt.hu/api/publication/2569368}, author = {Titkos, Tamás}, doi = {10.1007/s10474-014-0416-2}, journal-iso = {ACTA MATH HUNG}, journal = {ACTA MATHEMATICA HUNGARICA}, volume = {143}, unique-id = {2569368}, issn = {0236-5294}, abstract = {The aim of this paper is to generalize the theory of operator connections for nonnegative sesquilinear forms. As an application, we investigate the case of bounded finitely additive set functions. One of the most important connections in this setting is the parallel sum. We introduce this notion, and in addition, we present a Lebesgue-type decomposition theorem for such functions. © 2014 Akadémiai Kiadó, Budapest, Hungary.}, keywords = {Positive operator; Geometric mean; almost dominated part; nonnegative sesquilinear form; parallel sum; Lebesgue-type decomposition; Singular part; Gaussian mean; harmonic mean; finitely additive measure}, year = {2014}, eissn = {1588-2632}, pages = {515-533} }