A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

N.A.

Article Details

A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Authors:

N.A.

Publisher:

Istanbul University

Main Topics:

Pure Mathematics (Other)

Journal:

Istanbul Journal of Mathematics Vol.1 Issue 2, pp.48-56

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001311484

pISSN:

2980-3020

Keywords:

Abstract:

 Generalized trapezoid and trapezoid rules play an important role in approximating the Lebesgue integral in the case of scalarvalued functions defined on a finite interval. Motivated by this reason, in this paper we provided several norm error bounds in approximation the integral of continuous function of the convex combination of some tensorial products in terms of the corresponding tensorial generalized and trapezoid rules. The case of continuously differentiable functions is analysed in detail in the case when the derivative is bounded on a finite interval. Related results for the case when the absolute value of the derivative is convex is also provided. The important particular case for the operator exponential function is also considered and the corresponding norm inequalities revealed.

 Generalized trapezoid and trapezoid rules play an important role in approximating the Lebesgue integral in the case of scalarvalued functions defined on a finite interval. Motivated by this reason, in this paper we provided several norm error bounds in approximation the integral of continuous function of the convex combination of some tensorial products in terms of the corresponding tensorial generalized and trapezoid rules. The case of continuously differentiable functions is analysed in detail in the case when the derivative is bounded on a finite interval. Related results for the case when the absolute value of the derivative is convex is also provided. The important particular case for the operator exponential function is also considered and the corresponding norm inequalities revealed.

 Generalized trapezoid and trapezoid rules play an important role in approximating the Lebesgue integral in the case of scalarvalued functions defined on a finite interval. Motivated by this reason, in this paper we provided several norm error bounds in approximation the integral of continuous function of the convex combination of some tensorial products in terms of the corresponding tensorial generalized and trapezoid rules. The case of continuously differentiable functions is analysed in detail in the case when the derivative is bounded on a finite interval. Related results for the case when the absolute value of the derivative is convex is also provided. The important particular case for the operator exponential function is also considered and the corresponding norm inequalities revealed.

 Generalized trapezoid and trapezoid rules play an important role in approximating the Lebesgue integral in the case of scalarvalued functions defined on a finite interval. Motivated by this reason, in this paper we provided several norm error bounds in approximation the integral of continuous function of the convex combination of some tensorial products in terms of the corresponding tensorial generalized and trapezoid rules. The case of continuously differentiable functions is analysed in detail in the case when the derivative is bounded on a finite interval. Related results for the case when the absolute value of the derivative is convex is also provided. The important particular case for the operator exponential function is also considered and the corresponding norm inequalities revealed.

Article Details

A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Authors:

N.A.

Publisher:

Istanbul University

Main Topics:

Pure Mathematics (Other)

Journal:

Istanbul Journal of Mathematics Vol.1 Issue 2, pp.48-56

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001311484

pISSN:

2980-3020

tensorial product

selfadjoint operators

operator norm

trapezoid rule

convex functions

Issues

Article Details

A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces

Authors: N.A.

Publisher: Istanbul University

Main Topics: Pure Mathematics (Other)

Journal: Istanbul Journal of Mathematics Vol.1 Issue 2, pp.48-56

Document Type: Article

Publication Date: 12/2023

Document Language: English

Document ID (Org No.): 2001311484

pISSN: 2980-3020

tensorial product

selfadjoint operators

operator norm

trapezoid rule

convex functions

Issues

Authors:

N.A.

Publisher:

Istanbul University

Main Topics:

Pure Mathematics (Other)

Journal:

Istanbul Journal of Mathematics Vol.1 Issue 2, pp.48-56

Document Type:

Article

Publication Date:

12/2023

Document Language:

English

Document ID (Org No.):

2001311484

pISSN:

2980-3020