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Research Interests:

My primary interest is in functional Analysis. Mostly, my research problems concerns on Operator theories and algebras. Currently, I am  working in Multivariate operator theory. 

The following are my line of research:

1. Moment Problem: (With postdoc mentor Prof. B V Rajarama Bhat). Here, we want to understand operator valued sequences that admits various dilation and its connection with completely positive maps and integral representations.

2. Dilation Theory: Non-commuting operators.

3. Dilation theory: CP maps, CB maps and Quantum dynamical semigroups.

4. Semigroups: C*-algebras generated by Isometries, Wold decomposition, Coburn Theorem.

5. Function theory: Isometry, Wold-decomposition, Hardy space, RKHS, BLH-Theorem, Toeplitz operators.

6. M-ideals in operator spaces/algebras: (With my supervisor Prof. Anil K. Karn).

                                                                                    Publications:

• Functional Analysis:--------------------------------------------------------------------

4) A. Ghatak, Generalization of M-ideals in a non-unital ordered normed spaces, (Advances in Operator Theory), to appear.

3) A. Ghatak, A. K. Karn, Quantization of A_{0}(K)-spaces, (Operator and Matrix).

2)  A. Ghatak, A. K. Karn, CM-ideals and L^{1}-matricial split faces, accepted, (Acta. Math. Sezged). 

1) A. Ghatak, A. K. Karn,  M-ideals and split faces of the quasi-state spaces of a non-unital ordered Banach spaces,  (Positivity).

   Operator Algebras:------------------------------------------------------------------------

            4) Anindya Ghatak, Multiplier algebra of the the Fock space arising from left cancellative semigroups.

        3) Anindya Ghatak, Aryaman Sensarma, A Russo-Dye type Theorem and Stinespring type representation for invariant block multilinear completely positive maps, Communicated. 

    2) BV Rajarama Bhat, A. Ghatak, Santhosh Kumar, Unbounded CP-maps and Radon-Nikodym Theorem, Indag. Math. (arXiv:2004.12717v1).

        1) A. Ghatak, Santhosh Kumar, Unbounded Multilinear CP-maps and Radon-Nikodym Theorem, To appear in Linear and Multilinear Algebras.

Multivariate Operator  Theory:------------------------------------------------------------------------

 1) A. Ghatak, N. Rakshit, Jaydeb Sarkar, Manshi Surawanshi, Wold decomposition on twisted odometer semigroups, Preprint.     

  2) BV Rajarama Bhat, A. Ghatak, Santhosh Kumar,  Moment Dilations, Under preparation.

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Talk Delivered:

1.  Qunatization A_{0}(K)-spaces,  Postdoc symposium, ISI Bangalore,  2019

2.  Qunatization A_{0}(K)-spaces, Conference on Quantum groups and non commutative geometry, NISER,                          Bhubaneswar, India, 2018.

3.   M-ideals in non initial order normed spaces, Conference on functional analysis @IIT Bombay -2017. 

4.  M-ideals and ball remotality in ordered normed spaces, October 11, 2015 at NISER, Bhubaneswar, India.

5. Order theoretic properties of C*-algebras and its generalization, State of the art seminar (as a part of my Ph.D.  Programme), February 03, 2015 at NISER, Bhubaneswar, India.

6.  The characterization of Operator space, April 21, 2014 at NISER, Bhubaneswar, India.

7. Spectral decomposition of normal operators on Hilbert spaces, November 21, 2013, NISER, Bhubaneswar, India.

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Schools and Conferences Attended:

1. Quantum grops, NISER, Bhubaneswar.

2.  KBS fest,

3.                                                                                    IISER-Bhopal, India.

4.  February 20-22, 2019, Symposium on operator theory, IISC-Bangalore, India.

5.  December 13-19-2018, OTOA-2018, ISI Bangalore, India.

6.   June 25 - -July 21, 2018,  AIS Stochastic Processes, NISER (Bhubaneswar).

7.   March 05-10, 2018, Modern aspects of function theory Operator theory and Operator algebras, ISI-Bangalore.  

8.   January 15-19, 2018,  Conference on Quantum groups and non commutative geometry, NISER (Bhubaneswar), 2018.

9. October 12-15, 2017, Conference on Functional Analysis@ IIT Bombay-2017}, & IIT Bombay, India.

10.   December 13-22, 2016, OTOA-2016}, ISI Bangalore, India.

11. September 22-24, 2016, A Celebration of T. S. S. R. K. Rao's 60th Birthday,  ISI Bangalore, India.

12. February 18-22, 2016, Advances in Non Commutative Mathematics, ISI Bangalore, India.

13.   March 01 - 21, 2016, Advanced Instructional School in Operator Algebras and Operator Theory, Institute of  Mathematical Sciences, Chennai, India.

14.  December 08-20, 2014, ATMW PDE and Fourier Analysis.,  IIT Kanpur, India.

15.   May 01- 28, 2014, Annual Foundation School-Part II, CEMS, Department of Mathematics, SSJ Campus, Kumaun University, Almora, India.

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