• Communications of the Korean Mathematical Society
• /
• v.18 no.4
• /
• pp.669-676
• /
• 2003

In 1989, Rhaly [4] determined the spectrum of Rhaly operator $R_{a}$ on the Hilbert space ${\ell}_2$. In this paper Authors determine the spectrum of the Rhaly matrix $R_{a}$ as an operator on the space bvo with assumption $0\;<\;L\;=\;lim_n(n\;+\;1)a_n\;<\;\infty$.

• East Asian mathematical journal
• /
• v.18 no.1
• /
• pp.21-41
• /
• 2002

In this paper, we determine the spectrum of the Rhaly matrix $R_a$ as an operator on the space by, when $lim_n(n+1)a_n{\neq}0$ and exists.

• East Asian mathematical journal
• /
• v.23 no.2
• /
• pp.135-149
• /
• 2007

In 1975, Wenger [4] determined the fine spectra of $Ces{\grave{a}}ro$ operator $C_1$ on c, the space of convergent sequences. In [7], the spectrum of the Rhaly operators on $c_0$ and c, under the assumption that ${lim}\limits_{n{\rightarrow}{\infty}}(n+1)a_n\;=\;L\;{\neq}\;0$, has been determined. In this paper the author determine the fine spectra of the Rhaly matrix $R_a$ as an operator on the space c, with the same assumption.

• Bulletin of the Korean Mathematical Society
• /
• v.55 no.2
• /
• pp.673-674
• /
• 2018

Corrections are made for some examples following Theorem 2.2 in Posinormal terraced matrices, Bull. Korean Math. Soc. 46 (2009), no. 1, 117-123.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.3
• /
• pp.425-434
• /
• 2010

Here we see that the $p-Ces{\grave{a}}ro$ operators, the generalized $Ces{\grave{a}}ro$ operators of order one, the discrete generalized $Ces{\grave{a}}ro$ operators, and their adjoints are all posinormal operators on ${\ell}^2$, but many of these operators are not dominant, not normaloid, and not spectraloid. The question of dominance for $C_k$, the generalized $Ces{\grave{a}}ro$ operators of order one, remains unsettled when ${\frac{1}{2}}{\leq}k<1$, and that points to some general questions regarding terraced matrices. Sufficient conditions are given for a terraced matrix to be normaloid. Necessary conditions are given for terraced matrices to be dominant, spectraloid, and normaloid. A very brief new proof is given of the well-known result that $C_k$ is hyponormal when $k{\geq}1$.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.1
• /
• pp.117-123
• /
• 2009

This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ${\ell}^2$; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that $MM^*=M^*PM$ for some positive operator P on ${\ell}^2$; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint $M^*$ to be posinormal, and it is observed that, unless M is essentially trivial, $M^*$ cannot be hyponormal. A few examples are considered that exhibit special behavior.