Which subnormal Toeplitz operators are either normal or analytic?

We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos's Problem 5: Which subnormal block Toeplitz operators are either normal or analytic? We extend and prove Abrahamse's Theorem to the case of matrix-valued symbols; that is, we show that every subnormal block Toeplitz operator with bounded type symbol (i.e., a quotient of two analytic functions), whose co-analytic part has a "coprime decomposition," is normal or analytic. We also prove that the coprime decomposition condition is essential. Finally, we examine a well known conjecture, of whether every submormal Toeplitz operator with finite rank self-commutator is normal or analytic.Comment: Final version, accepted for publication in Journal of Functional Analysi

Hyponormality and Subnormality of Block Toeplitz Operators

In this paper we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space $H^2_{\mathbb{C}^n}$ of the unit circle. Firstly, we establish a tractable and explicit criterion on the hyponormality of block Toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator. Secondly, we consider the gap between hyponormality and subnormality for block Toeplitz operators. This is closely related to Halmos's Problem 5: Is every subnormal Toeplitz operator either normal or analytic? We show that if $\Phi$ is a matrix-valued rational function whose co-analytic part has a coprime factorization then every hyponormal Toeplitz operator $T_{\Phi}$ whose square is also hyponormal must be either normal or analytic. Thirdly, using the subnormal theory of block Toeplitz operators, we give an answer to the following "Toeplitz completion" problem: Find the unspecified Toeplitz entries of the partial block Toeplitz matrix A:=[U^*& ? ?&U^*] so that $A$ becomes subnormal, where $U$ is the unilateral shift on $H^2$.Comment: Final version, accepted for publication in Advances in Mathematic

A gap between hyponormality and subnormality for block Toeplitz operators

AbstractThis paper concerns a gap between hyponormality and subnormality for block Toeplitz operators. We show that there is no gap between 2-hyponormality and subnormality for a certain class of trigonometric block Toeplitz operators (e.g., its co-analytic outer coefficient is invertible). In addition we consider the extremal cases for the hyponormality of trigonometric block Toeplitz operators: in this case, hyponormality and normality coincide

Effect Of Changes In The Korean Accounting Environment On The Productivity Of Accounting Firms

To investigate how changes in the accounting environment in Korea affect firm productivity, this study analyzes productivity by firm size and labor type from 2000 to 2014, using a Cobb–Douglas production function. We find that (1) the greater the management advisory (tax) revenue, the greater the total revenue in large (small) accounting firms; and (2) marginal revenue is greatest for partners, followed by certified public accountants and general employees. In particular, partners’ contribution to large accounting firms improved after 2007, whereas general employees made a significant positive contribution to total revenue before 2007

To the Edge of M87 and Beyond: Spectroscopy of Intracluster Globular Clusters and Ultra Compact Dwarfs in the Virgo Cluster

We present the results from a wide-field spectroscopic survey of globular clusters (GCs) in the Virgo Cluster. We obtain spectra for 201 GCs and 55 ultracompact dwarfs (UCDs) using the Hectospec on the Multiple Mirror Telescope, and derive their radial velocities. We identify 46 genuine intracluster GCs (IGCs), not associated with any Virgo galaxies, using the 3D GMM test on the spatial and radial velocity distribution.They are located at the projected distance 200 kpc $\lesssim$ R $\lesssim$ 500 kpc from the center of M87. The radial velocity distribution of these IGCs shows two peaks, one at $v_{\rm r}$ = 1023 km s$^{-1}$ associated with the Virgo main body, and another at $v_{\rm r}$ = 36 km s$^{-1}$ associated with the infalling structure. The velocity dispersion of the IGCs in the Virgo main body is $\sigma_{\rm{GC}} \sim$ 314 km s$^{-1}$, which is smoothly connected to the velocity dispersion profile of M87 GCs, but much lower than that of dwarf galaxies in the same survey field, $\sigma_{\rm{dwarf}} \sim$ 608 km s$^{-1}$. The UCDs are more centrally concentrated on massive galaxies, M87, M86, and M84. The radial velocity dispersion of the UCD system is much smaller than that of dwarf galaxies. Our results confirm the large-scale distribution of Virgo IGCs indicated by previous photometric surveys. The color distribution of the confirmed IGCs shows a bimodality similar to that of M87 GCs. This indicates that most IGCs are stripped off from dwarf galaxies and some from massive galaxies in the Virgo.Comment: 19 pages, 20 figures, 8 tables, accepted for publication in Ap

Persistent Genital Swelling after Hydrocele Ligation in a Patient Receiving Continuous Ambulatory Peritoneal Dialysis

We report a case of genital swelling in a patient receiving continuous ambulatory peritoneal dialysis. A physical examination did not identify any defect. Ultrasonography revealed a large hydrocele, and surgical repair brought resolution of the genital swelling. Two months later, however, the genital swelling had recurred and was not improved until peritoneal dialysis was replaced by hemodialysis 3 months later