• Kyungpook Mathematical Journal
• /
• v.62 no.4
• /
• pp.751-767
• /
• 2022

This paper deals with the Paneitz-Branson operator in compact Riemannian manifolds with negative Yamabe invariant. We start off by providing a new criterion for the positivity of the Paneitz-Branson operator when the Yamabe invariant of the manifold is negative. Another result stated in this paper is about the existence of a metric on a manifold of dimension 5 such that the Paneitz-Branson operator has multiple negative eigenvalues. Finally, we provide new inequalities related to the upper bound of the mean value of the Q-curvature.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.2
• /
• pp.305-313
• /
• 2010

In this paper, we prove that if $T{\in}L$(X) is a generalized scalar operator then Ker $T^p$ is the quasi-nilpotent part of T for some positive integer $p{\in}{\mathbb{N}}$. Moreover, we prove that a generalized scalar operator with finite spectrum is algebraic. In particular, a quasi-nilpotent generalized scalar operator is nilpotent.

• Journal of the Korean Mathematical Society
• /
• v.38 no.6
• /
• pp.1157-1166
• /
• 2001

This paper answers some old questions about approximate similarity and raises new ones. We provide positive evidence and a technique for finding negative evidence on the question of whether approximate similarity is the equivalence relation generated by approximate equivalence and similarity.

• Communications of the Korean Mathematical Society
• /
• v.23 no.4
• /
• pp.541-548
• /
• 2008

For a completely bounded linear maps between operator spaces, we introduce numbers which measure the degree of injectivity and subjectivity. The number measuring the injectivity is an operator space analogue of the minimum modulus of a linear map in normed spaces.

• Korean Journal of Mathematics
• /
• v.8 no.2
• /
• pp.111-119
• /
• 2000

For a linear operator Q from $R^d$ into $R^d$. ${\alpha}$ > 0 and 0 < $b$ < 1, the Gaussian (Q, $b$, ${\alpha}$)-semi-stability of probability measures on $R^d$ is investigated.

• Communications of the Korean Mathematical Society
• /
• v.17 no.1
• /
• pp.21-29
• /
• 2002

The existence of the operator-valued Feynman integral was established when a Wiener functional is given by a Fourier transform of complex Borel measures. In this paper, we investigate the stability of the Feynman integral with respect to the measures.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.3
• /
• pp.681-698
• /
• 2016

In this paper, we investigate relative essential spectra of $2{\times}2$ block operator matrix using the Fredholm perturbation theory. Furthermore, an example for two-group transport equations is presented to illustrate the validity of the main results.

• Korean Journal of Mathematics
• /
• v.24 no.1
• /
• pp.15-25
• /
• 2016

We obtain some estimations of the essential norm of a pull back operator induced by quasi-symmetric homeomorphisms. As a corollary, we deduce the compactness criterion of this operator.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.171-181
• /
• 1999

In this note, we will prove that the operator-valued function space integral as an operator from $L_p\;to\;L_{p'}$ (1

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.509-520
• /
• 2020

We study the Toeplitz operators on the holomorphic and pluriharmonic Dirichlet spaces of the polydisk in terms of when Toeplitz operator is Fredholm operator there. Consequently, we describe the essential spectrum of Toeplitz operators.