Moment Problems in Hereditary Function Spaces

Abstract We introduce a concept of hereditary set of multi-indices, and consider vector spaces of functions generated by families associated to such sets of multi-indices, called hereditary function spaces. Existence and uniquenes of representing measures for some abstract truncated moment problems are investigated in this framework, by adapting the concept of idempotent and that of dimensional stability, and using some techniques involving C*-algebras and commuting self-adjoint multiplication operators.

Download Full-text

Carleson Measures, Riemann–Stieltjes and Multiplication Operators on a General Family of Function Spaces

Integral Equations and Operator Theory ◽

10.1007/s00020-014-2124-2 ◽

2014 ◽

Vol 78 (4) ◽

pp. 483-514 ◽

Cited By ~ 11

Author(s):

Jordi Pau ◽

Ruhan Zhao

Keyword(s):

Function Spaces ◽

Carleson Measures ◽

Multiplication Operators ◽

General Family

Download Full-text

The multiplication operators on some analytic function spaces of the unit ball

Proceedings - Mathematical Sciences ◽

10.1007/s12044-013-0110-2 ◽

2013 ◽

Vol 123 (1) ◽

pp. 33-46

Author(s):

BENOÎT F SEHBA

Keyword(s):

Analytic Function ◽

Unit Ball ◽

Function Spaces ◽

Multiplication Operators ◽

Analytic Function Spaces

Download Full-text

Compact-Friendly Multiplication Operators on Banach Function Spaces

Journal of Functional Analysis ◽

10.1006/jfan.2001.3931 ◽

2002 ◽

Vol 192 (2) ◽

pp. 517-523 ◽

Cited By ~ 3

Author(s):

G.G Sirotkin

Keyword(s):

Function Spaces ◽

Multiplication Operators ◽

Banach Function Spaces

Download Full-text

Multiplication operators on vector-valued function spaces

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-2013-11603-5 ◽

2013 ◽

Vol 141 (10) ◽

pp. 3501-3513 ◽

Cited By ~ 1

Author(s):

Hülya Duru ◽

Arkady Kitover ◽

Mehmet Orhon

Keyword(s):

Function Spaces ◽

Multiplication Operators ◽

Vector Valued Function ◽

Vector Valued

Download Full-text

Dimensional stability in truncated moment problems

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2011.11.063 ◽

2012 ◽

Vol 388 (1) ◽

pp. 219-230 ◽

Cited By ~ 5

Author(s):

Florian-Horia Vasilescu

Keyword(s):

Dimensional Stability ◽

Moment Problems

Download Full-text

Matrix multiplication operators on Banach function spaces

Proceedings of the Indian Academy of Sciences - Section A ◽

10.1007/bf02829740 ◽

2006 ◽

Vol 116 (1) ◽

pp. 71-81 ◽

Cited By ~ 5

Author(s):

H. Hudzik ◽

Rajeev Kumar ◽

Romesh Kumar

Keyword(s):

Matrix Multiplication ◽

Function Spaces ◽

Multiplication Operators ◽

Banach Function Spaces

Download Full-text

Fixed points results in modular vector spaces with applications to quantum operations and Markov operators

Carpathian Journal of Mathematics ◽

10.37193/cjm.2020.02.11 ◽

2020 ◽

Vol 36 (2) ◽

pp. 277-286

Author(s):

MOHAMED AMINE KHAMSI ◽

◽

POOM KUMAM ◽

UMAR BATSARI YUSUF ◽

◽

...

Keyword(s):

Fixed Point ◽

Fixed Point Theory ◽

Order Relation ◽

Modular Function ◽

Point Theory ◽

Function Spaces ◽

Vector Spaces ◽

Markov Operators ◽

Modular Spaces ◽

Modular Function Spaces

Recently, researchers are showing more interest on both modular vector spaces and modular function spaces. Looking at the number of results it is pertinent to say that, exploration in this direction especially in the area of fixed point theory and applications is still ongoing, many good results can still be unveiled. As a contribution from our part, we study some fixed point results in modular vector spaces associated with order relation. As an application, we were able to study the existence of fixed point(s) of both depolarizing quantum operation and Markov operators through modular functions/modular spaces. The awareness on the importance of quantum theory and Economics globally were the sole motivations of the application choices in our work. Our work complement the existing results. In fact, it adds to the number of application areas that modular vector/function spaces covered.

Download Full-text