Numerical radius and p-Schatten norm inequalities for power series of operators in Hilbert spaces

Sever Dragomır

Makale detayları

Numerical radius and p-Schatten norm inequalities for power series of operators in Hilbert spaces

Yazarlar:

Sever Dragomır

Yayıncı:

Ankara University

Ana Başlıklar:

Complex Systems in Mathematics | Approximation Theory and Asymptotic Methods

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 2, pp.365-390

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001318077

pISSN:

1303-5991

Anahtar kelimeler:

Özet:

 Let H be a complex Hilbert space. Assume that the power series with complex coefficients fz:sumnolimits_k0infty a_kzk is convergent on the open disk D0,R,f_az:sumnolimits_k0inftyleftvert a_krightvert zk that has the same radius of convergence R and A,B,Cin BH with leftVert ArightVert  R, then we have the following Schwarz type inequality  leftvert leftlangle Cast AfABx,yrightrangle rightvert leq f_aleftVert ArightVert leftlangle leftvert leftvert Arightvert alpha Brightvert 2x,xrightrangle 12leftlangle leftvert leftvert Aast rightvert 1-alpha Crightvert 2y,yrightrangle 12  for alpha in lbrack 0,1 and x,yin H. Some natural applications for numerical radius and p-Schatten norm are also provided.

 Let H be a complex Hilbert space. Assume that the power series with complex coefficients fz:sumnolimits_k0infty a_kzk is convergent on the open disk D0,R,f_az:sumnolimits_k0inftyleftvert a_krightvert zk that has the same radius of convergence R and A,B,Cin BH with leftVert ArightVert  R, then we have the following Schwarz type inequality  leftvert leftlangle Cast AfABx,yrightrangle rightvert leq f_aleftVert ArightVert leftlangle leftvert leftvert Arightvert alpha Brightvert 2x,xrightrangle 12leftlangle leftvert leftvert Aast rightvert 1-alpha Crightvert 2y,yrightrangle 12  for alpha in lbrack 0,1 and x,yin H. Some natural applications for numerical radius and p-Schatten norm are also provided.

 Let H be a complex Hilbert space. Assume that the power series with complex coefficients fz:sumnolimits_k0infty a_kzk is convergent on the open disk D0,R,f_az:sumnolimits_k0inftyleftvert a_krightvert zk that has the same radius of convergence R and A,B,Cin BH with leftVert ArightVert  R, then we have the following Schwarz type inequality  leftvert leftlangle Cast AfABx,yrightrangle rightvert leq f_aleftVert ArightVert leftlangle leftvert leftvert Arightvert alpha Brightvert 2x,xrightrangle 12leftlangle leftvert leftvert Aast rightvert 1-alpha Crightvert 2y,yrightrangle 12  for alpha in lbrack 0,1 and x,yin H. Some natural applications for numerical radius and p-Schatten norm are also provided.

 Let H be a complex Hilbert space. Assume that the power series with complex coefficients fz:sumnolimits_k0infty a_kzk is convergent on the open disk D0,R,f_az:sumnolimits_k0inftyleftvert a_krightvert zk that has the same radius of convergence R and A,B,Cin BH with leftVert ArightVert  R, then we have the following Schwarz type inequality  leftvert leftlangle Cast AfABx,yrightrangle rightvert leq f_aleftVert ArightVert leftlangle leftvert leftvert Arightvert alpha Brightvert 2x,xrightrangle 12leftlangle leftvert leftvert Aast rightvert 1-alpha Crightvert 2y,yrightrangle 12  for alpha in lbrack 0,1 and x,yin H. Some natural applications for numerical radius and p-Schatten norm are also provided.

Makale detayları

Numerical radius and p-Schatten norm inequalities for power series of operators in Hilbert spaces

Yazarlar:

Sever Dragomır

Yayıncı:

Ankara University

Ana Başlıklar:

Complex Systems in Mathematics | Approximation Theory and Asymptotic Methods

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 2, pp.365-390

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001318077

pISSN:

1303-5991

Vector inequality

bounded operators

Aluthge transform

Dougal transform

partial isometry

numerical radius

p-Schatten norm

Sayı

Makale detayları

Yazarlar: Sever Dragomır

Yayıncı: Ankara University

Ana Başlıklar: Complex Systems in Mathematics | Approximation Theory and Asymptotic Methods

Dergi: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 2, pp.365-390

Belge Tipi: Makale

Yayın Tarihi: 6/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001318077

pISSN: 1303-5991

Sayı

Yazarlar:

Sever Dragomır

Yayıncı:

Ankara University

Ana Başlıklar:

Complex Systems in Mathematics | Approximation Theory and Asymptotic Methods

Dergi:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.73 Issue 2, pp.365-390

Belge Tipi:

Makale

Yayın Tarihi:

6/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001318077

pISSN:

1303-5991