TEW - Functional Analysis (2021)

Speakers and Syllabus

 

Name of the Speaker with affiliation

No. of Lectures

Detailed Syllabus

1.Prof. Thamban Nair,
IIT Madras

Prof. Pradipta Bandopadhyay.
ISI, Kolkatta

9 hours

A quick Introduction to Banach spaces and bounded linear maps, Uniform boundedness principle (with some applications to classical analysis), Open mapping theorem (Closed graph theorem), Hilbert space (orthonormal systems, orthogonal basis, bounded linear maps), Gram Schmidt orthogonalisation process (applied to certain concrete sequences in spaces), Projection Theorem, Riesz representation theorem for Hilbert space

2.Prof. Sameer Chavan,
Indian Institute of Technology (IIT) Kanpur.

5 hours

Unitary operators and the unitary group on Hilbert space, Spectral theorem self adjoint operators, Hilbert space methods in function theory (including Maximum modulus theorem, Muntz-Szas theorem for

 

3.Dr. Surinderpal Singh
Panjab University, Chandigarh

6 hours

Arzela-Ascoli theorem, Banach-Mazurkiewicz theorem on the size of C\ND. Hausdorff -Alexandroff theorem: (Each compact metrics space as a quotient of the Cantor set), Banach Mazur theorem (C[0,1] as a universal separable Banach space), Computation of the dual of C(K) for K = [0,1] and K = compact subset of ℝ as a prelude to the Riesz Representation Theorem for C(K), K a compact metric space.

 

4.Prof. M. A. Sofi
JKIMS (Kashmir University) Srinagar

7 hours

Background material and motivation, Weak, weak* topologies on Banach spaces, Banach - Alaoglu theorem and applications, Analytic and geometric forms of the HBT and their equivalence, Applications of HBT, Invariant form of HB-theorem, Construction of universal, finitely additive invariant measures on ℝ and .

References:

  1. (Prof. Sameer Chavan)
    (i) Operator Analysis: Hilbert Space Methods in Complex Analysis, J. Agler, J. E. McCarthy,N. J. Young, Cambridge University Press,2020.
    (ii) Simon, Operator Theory. A Comprehensive Course in Analysis, Parts I andV, American Mathematical Society, Providence, RI, 2015,
    (iii) J.B. Conway, A course in Functional Analysis, Springer, 2006.

  1. (Prof. Pradipta Bandopadhyay)

  1. S. Kumaresan and D. Sukumar, Functional Analysis, Narosa.

  2. R. Bhatia, Notes on Functional Analysis, Hindustan Book Agency

  3. M. Fabian et al, Banach Space Theory, Springer Verlag

 

  1. Dr. Surinder Pal Singh Kainth)
    (a) Arzela Ascoli theorem (reference (iv)).
    (b) Hausdorff–Alexandroff Theorem (Proposition 2.3, reference (ii))
    (c)     Riesz Representation Theorem for C(K) when K = [0,1] or a compact subset of ℝ (reference (i)).
    (d)     Riesz Representation Theorem for C(K) when K is a compact metric space (reference (ii))
    (e) Banach-Mazur Theorem. (page 18 of reference (iii)).

References:

  1. Rafael del Rio, A. L. Franco, and J. A. Lara; An approach to F. Riesz representation Theorem, CUBO A Mathematical Journal, 20 (2), 2018, 1-12.
  2. V. S. Sunder; The Riesz Representation Theorem, Indian Journal of Pure and Applied Mathematics, 39 (6), 2008, 467-481.
  3. F. Albiac, N. J. Kalton; Topics in Banach space theory, Springer, 2006
  4. W. Rudin; Principles of mathematical analysis, McGraw-Hill, 1976. 

 

  1. Prof. M. A. Sofi

  1. M. Fabian et al, Banach Space Theory, Springer Verlag

  2. Some Problems in functional analysis inspired by Hahn Banach theorem, Annals of Functional Analysis, 5(2014) no.2, 1-29.

  3. Weak* topology, compactness and the existence of certain invariant measures, Mathematics Newsletter (Ramanujan Math Soc), 31(2), 49-61, Sept. 2020.

 

Tutors:

S. No.

Name

Affiliation

1

Dr. Ramiz Reza/Dr. Nisar A. Lone

IIT Jammu/JKIMS, Srinagar

2

Dr. Ajay Kumar

IIT Jammu

Guest Speaker:

S. No.

Name

Affiliation

1

Prof. Thamban Nair

Department of Mathematics, IIT Madras

 

Note: All the speakers shall be expected to provide notes of their lectures.

Time Table

Time-table-I (Sundays):

Day

Date

Lecture-1

(10-11.30)

Tea

(11.35-11.55)

Lecturer 2

(12.00–1.00)

Lunch

(1.30 – 3.00)

Lecture 3

(3.00-4.00)

Discussion

(4.15-5:15)

Tea & Snacks
(5.30 – 6.00)

 

 

(Speaker’s name)

 

(Speaker’s name)

 

(Speaker’s name)

(Tutor’s name)

 

Sun

Nov.28

TN

Tea

TN

Lunch

SC

Discussion (TN+

 

Sun

Decc.5

MAS

Tea

TN

Lunch

Guest Lecture

Discussion (SC+

Snacks

Sun

Dec.12

Discussion (SPS)

Tea

MAS

Lunch

Panel Discussion on Teaching and Research in UG-Maths (All the speakers + participants)

Snacks

 

Time Table-II (Weekdays)

 

Day

Date

Lecture /Discussion
(6.00-7.30)

Mon

Nov.29

SC

Tue

Nov.30

SC

Wed

Dec.1

PB

Thurs

Dec.2

PB

Fri

Dec.3

PB

Sat

Dec.4

MAS

Mon

Dec.6

MAS

Tue

Dec.7

Discussion (MAS)

Wed

Dec.8

SPS

Thurs

Dec.9

SPS

Fri

Dec.10

SPS

Sat

Dec.11

Guest Lecture (TN)

 

 

 

Speakers

 

TN: Prof. Thamban Nair (IIT Madras)

 

PB: Prof. Pradipta Bandopadhyay (ISI, Kolkatta)

 

SC: Prof. Sameer Chavan (IIT Kanpur)

 

SPS: Dr. Surinder Pal Singh Kainth (Panjab University, Chandigarh)

 

MAS: Prof. M A Sofi, JKIMS (Kashmir University), Srinagar

 

 

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