کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4599362 | 1631132 | 2014 | 20 صفحه PDF | دانلود رایگان |
In this paper we present a new weighted, multivariable operator mean of positive definite operators over an arbitrary Hilbert space which provides us the first generally applicable extension of the classical Kubo–Ando theory of 2-variable operator means. The construction is a weighted extension of the Bini–Meini–Poloni symmetrization process originally given for the matrix geometric mean. Here to be able to consider such an iterative procedure, we need a weighted version of every Kubo–Ando mean in two variables. Therefore we also give a new construction for two arbitrary positive operators on a possibly infinite dimensional Hilbert space that provides weighted counterparts to every (not-necessarily symmetric) Kubo–Ando mean and also agrees with the most well known weighted operator means.
Journal: Linear Algebra and its Applications - Volume 463, 15 December 2014, Pages 134–153