EXTREME STATES, OPERATOR SPACES AND TERNARY
RINGS OF OPERATORS
A. K. Vijayarajan
Kerala School of Mathematics, Kozhikode 673 571 (India).
E-mail:vijay@ksom.res.in
ORCID:0000-0001-5084-0567
Reception: 29/09/2022 Acceptance: 14/10/2022 Publication: 29/12/2022
Suggested citation:
A.K. Vijayarajan (2022). Extrem states, operator spaces and ternary rings of operators. 3C TIC. Cuadernos de desarrollo
aplicados a las TIC,11 (2), 124-134. https://doi.org/10.17993/3ctic.2022.112.124-134
https://doi.org/10.17993/3ctic.2022.112.124-134
ABSTRACT
In this survey article on extreme states of operator spaces in
C¡
-algebras and related ternary ring of
operators an extension result for rectangular operator extreme states on operator spaces in ternary rings
of operators is discussed. We also observe that in the spacial case of operator spaces in rectangular
matrix spaces, rectangular extreme states are conjugates of inclusion or identity maps implemented by
isometries or unitaries. A characterization result for operator spaces of matrices for which the inclusion
map is an extreme state is deduced using the above mentioned results.
KEYWORDS
keyword 1, Keyword 2,...
https://doi.org/10.17993/3ctic.2022.112.124-134
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
124
EXTREME STATES, OPERATOR SPACES AND TERNARY
RINGS OF OPERATORS
A. K. Vijayarajan
Kerala School of Mathematics, Kozhikode 673 571 (India).
E-mail:vijay@ksom.res.in
ORCID:0000-0001-5084-0567
Reception: 29/09/2022 Acceptance: 14/10/2022 Publication: 29/12/2022
Suggested citation:
A.K. Vijayarajan (2022). Extrem states, operator spaces and ternary rings of operators. 3C TIC. Cuadernos de desarrollo
aplicados a las TIC,11 (2), 124-134. https://doi.org/10.17993/3ctic.2022.112.124-134
https://doi.org/10.17993/3ctic.2022.112.124-134
ABSTRACT
In this survey article on extreme states of operator spaces in
C¡
-algebras and related ternary ring of
operators an extension result for rectangular operator extreme states on operator spaces in ternary rings
of operators is discussed. We also observe that in the spacial case of operator spaces in rectangular
matrix spaces, rectangular extreme states are conjugates of inclusion or identity maps implemented by
isometries or unitaries. A characterization result for operator spaces of matrices for which the inclusion
map is an extreme state is deduced using the above mentioned results.
KEYWORDS
keyword 1, Keyword 2,...
https://doi.org/10.17993/3ctic.2022.112.124-134
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
125