Opuscula Math. 33, no. 2 (2013), 283-291
http://dx.doi.org/10.7494/OpMath.2013.33.2.283

Opuscula Mathematica

# Inequalities for regularized determinants of operators with the Nakano type modulars

Michael Gil'

Abstract. Let $$\{p_k\}$$ be a nondecreasing sequence of integers, and $$A$$ be a compact operator in a Hilbert space whose eigenvalues and singular values are $$\lambda_k(A)$$ and $$s_k(A)$$ $$(k=1, 2, .... )$$, respectively. We establish upper and lower bounds for the regularized determinant $\prod_{k=1}^\infty (1-\lambda_k(A)){\rm exp}\;[\sum_{m=1}^{p_k-1} \frac{\lambda_k^m(A)}{m}],\mbox{ assuming that } \sum_{j=1}^{\infty} \frac{s_j^{p_j}(A/c)}{p_j}\lt \infty$ for a constant $$c\in (0,1)$$.

Keywords: Hilbert space, compact operators, regularized determinant, Nakano type modular.

Mathematics Subject Classification: 47B10, 47A55.

Full text (pdf)

• Michael Gil'
• Ben Gurion University of the Negev, Department of Mathematics, P.O. Box 653, Beer-Sheva 84105, Israel
• Received: 2012-11-12.
• Revised: 2012-12-11.
• Accepted: 2012-12-12.

Cite this article as:
Michael Gil', Inequalities for regularized determinants of operators with the Nakano type modulars, Opuscula Math. 33, no. 2 (2013), 283-291, http://dx.doi.org/10.7494/OpMath.2013.33.2.283

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.