On $f$-connections of positive definite matrices

Niezgoda, Marek

doi:10.15352/afa/1396833510

Ann. Funct. Anal.

2014

DOI: 10.15352/afa/1396833510

|View full text |Cite

On $f$-connections of positive definite matrices

Marek Niezgoda¹

Abstract: In this paper, by using Mond-Pečarić method we provide some inequalities for connections of positive definite matrices. Next, we discuss specifications of the obtained results for some special cases. In doing so, we use α-arithmetic, α-geometric and α-harmonic operator means.

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2014

2015

Publication Types

Select...

Article2

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 12 publications

(17 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

Inequalities for relative operator entropies

Kluza

Niezgoda

2014

ELA

View full text Add to dashboard Cite

In this paper, operator inequalities are provided for operator entropies transformed by a strictly positive linear map. Some results by Furuichi et al. [S. Furuichi, K. Yanagi, and K. Kuriyama. A note on operator inequalities of Tsallis relative operator entropy. Linear Algebra Appl., 407:19â31, 2005.], Furuta [T. Furuta. Two reverse inequalities associated with Tsallis relative operator entropy via generalized Kantorovich constant and their applications. Linear Algebra Appl., 412:526â537, 2006.], and Zou [L. Zou. Operator inequalities associated with Tsallis relative operator entropy. Math. Inequal. Appl., 18:401â406, 2015.] are extended. In particular, the obtained inequalities are specified for relative operator entropy and Tsallis relative operator entropy. In addition, some bounds for generalized relative operator entropy are established.

show abstract

Inequalities for relative operator entropies

Kluza

Niezgoda

2014

ELA

View full text Add to dashboard Cite

show abstract

On (T,f)-connections of matrices and generalized inverses of linear operators

Niezgoda

2015

ELA

View full text Add to dashboard Cite

In this note, generalized connections Ï_{T ,f} are investigated, where AÏ_{T ,f} B = T_Af(T_A)^â(B) for positive semidefinite matrix A and hermitian matrix B, and operator monotone function f : J â R on an interval J â R. Here the symbol (T_A)^â denotes a reflexive generalized inverse of a positive bounded linear operator T_A. The problem of estimating a given generalized connection by other ones is studied. The obtained results are specified for special cases of Î±-arithmetic, Î±-geometric and Î±-harmonic operator means.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

On $f$-connections of positive definite matrices

Abstract: In this paper, by using Mond-Pečarić method we provide some inequalities for connections of positive definite matrices. Next, we discuss specifications of the obtained results for some special cases. In doing so, we use α-arithmetic, α-geometric and α-harmonic operator means.

Cited by 2 publications

References 12 publications

Inequalities for relative operator entropies

Inequalities for relative operator entropies

On (T,f)-connections of matrices and generalized inverses of linear operators

Contact Info

Product

Resources

About