+91-674-249-4082

Submitted by anilkarn on 8 April, 2019 - 12:52

Date/Time:

Tuesday, April 16, 2019 - 15:30 to 16:30

Venue:

Mathematics Seminar Room

Speaker:

Anindya Ghatak

Affiliation:

NISER

Title:

Quantization of $A_{0}(K)$-spaces and $M$-ideals in matrix ordered spaces

Abstract: The theory of $M$-ideals in Banach spaces as well as in operator spaces is one of the important areas of research. It is well known from the literature that order structures and compact convex sets play a significant role in this area. Especially, the characterization of $M$-ideals in $A(K)$-spaces in terms of split face of the compact convex set $K$, established by Anderson and Alfsen, is a classical theorem of great importance.In this thesis, we have characterized $M$-ideal in order smooth $\infty$-normed spaces in terms of split faces of the quasi-state spaces. Also, we discuss the complete $M$-ideals in matricially order smooth $\infty$-normed spaces. For $p\neq \infty$, we introduce the notion of ideals, smooth $p$-order ideals to initiate the study of ideals in order smooth $p$-normedspaces.We introduce the notion of an $L^{1}$-matrix convex set in $*$-locally convex space. We show that $\{A_{0}(K_{n}, M_{n}(E))\}$(the `quantized functional space’) is a $\mathrm{C}^*$-ordered operator space. Conversely, every $\mathrm{C}^*$-ordered operator space is complete isometrically, completely isomorphic to $\{A_{0}(Q_{n}(V) M_{n}(V))\}$, where $Q_{n}(V)$ is the quasi-state space of $M_{n}(V)$ (in the matrix duality).

**School of Mathematical Sciences**

NISER, PO- Bhimpur-Padanpur, Via- Jatni, District- Khurda, Odisha, India, PIN- 752050

Tel: +91-674-249-4081

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