Showing papers in "Kyungpook Mathematical Journal in 2018"
TL;DR: In this paper, the authors studied 2 × 2 matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the (1, 1) entry has a nontrivial hyperinvariant subspace.
Abstract: In a previous paper, the authors of this paper studied 2× 2 matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the the (1, 1) entry has a nontrivial hyperinvariant subspace. We were able to show, in certain cases, that the 2× 2 matrix itself has a nontrivial hyperinvariant subspace. This generalized two earlier nice theorems of H. J. Kim from 2011 and 2012, and made some progress toward a solution of a problem that has been open for 45 years. In this paper we continue our investigation of such 2 × 2 operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.
4 citations
3 citations
TL;DR: In this article, a new approach to solving the 2-variable subnormal completion problem (SCP for short) was given, which extends the notion of recursively generated weighted shifts, introduced by R. Curto and L. Fialkow, to 2-variate case.
Abstract: In this paper, we give a new approach to solving the 2-variable subnormal completion problem (SCP for short). To this aim, we extend the notion of recursively generated weighted shifts, introduced by R. Curto and L. Fialkow, to 2-variable case. We next provide ”concrete” necessary and sufficient conditions for the existence of solutions to the 2-variable SCP with minimal Berger measure. Furthermore, a short alternative proof to the propagation phenomena, for the subnormal weighted shifts in 2-variable, is given.
1 citations
1 citations
TL;DR: In this article, the authors established relationship between continued fraction U(−q) of order 12 and Ramanujan's cubic continued fraction G(− q) and G(q) for n = 1, 2, 3, 5 and 7.
Abstract: In the present paper, we establish relationship between continued fraction U(−q) of order 12 and Ramanujan’s cubic continued fraction G(−q) and G(q) for n = 1, 2, 3, 5 and 7. Also we evaluate U(q) and U(−q) by using two parameters for Ramanujan’s theta-functions and their explicit values.