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DOI :10.26650/ijmath.2023.00006   IUP :10.26650/ijmath.2023.00006    Full Text (PDF)

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

Silvestru Sever Dragomir

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.

Keywords: tensorial product, selfadjoint operators, operator norm, trapezoid rule, convex functions

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References

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Citations

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APA

Dragomir, S.S. (2023). A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces. Istanbul Journal of Mathematics, 1(2), 48-56. https://doi.org/10.26650/ijmath.2023.00006


AMA

Dragomir S S. A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces. Istanbul Journal of Mathematics. 2023;1(2):48-56. https://doi.org/10.26650/ijmath.2023.00006


ABNT

Dragomir, S.S. A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces. Istanbul Journal of Mathematics, [Publisher Location], v. 1, n. 2, p. 48-56, 2023.


Chicago: Author-Date Style

Dragomir, Silvestru Sever,. 2023. “A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces.” Istanbul Journal of Mathematics 1, no. 2: 48-56. https://doi.org/10.26650/ijmath.2023.00006


Chicago: Humanities Style

Dragomir, Silvestru Sever,. “A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces.” Istanbul Journal of Mathematics 1, no. 2 (May. 2024): 48-56. https://doi.org/10.26650/ijmath.2023.00006


Harvard: Australian Style

Dragomir, SS 2023, 'A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces', Istanbul Journal of Mathematics, vol. 1, no. 2, pp. 48-56, viewed 18 May. 2024, https://doi.org/10.26650/ijmath.2023.00006


Harvard: Author-Date Style

Dragomir, S.S. (2023) ‘A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces’, Istanbul Journal of Mathematics, 1(2), pp. 48-56. https://doi.org/10.26650/ijmath.2023.00006 (18 May. 2024).


MLA

Dragomir, Silvestru Sever,. “A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces.” Istanbul Journal of Mathematics, vol. 1, no. 2, 2023, pp. 48-56. [Database Container], https://doi.org/10.26650/ijmath.2023.00006


Vancouver

Dragomir SS. A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces. Istanbul Journal of Mathematics [Internet]. 18 May. 2024 [cited 18 May. 2024];1(2):48-56. Available from: https://doi.org/10.26650/ijmath.2023.00006 doi: 10.26650/ijmath.2023.00006


ISNAD

Dragomir, SilvestruSever. “A Trapezoid Type Tensorial Norm Inequality for Continuous Functions of Selfadjoint Operators in Hilbert Spaces”. Istanbul Journal of Mathematics 1/2 (May. 2024): 48-56. https://doi.org/10.26650/ijmath.2023.00006



TIMELINE


Submitted19.09.2023
Accepted06.11.2023
Published Online18.12.2023

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