Download Original PDF
Get the official Barkatullah University print version scanned document.
đ¤ Help Your Juniors!
Have previous year question papers that aren't on our website? Help the next batch of students by sending them to us! With your consent, we will proudly feature your name as a Top Contributor on our platform.
Submit Papers đŠCD-499
M.A./M.Sc. IVth Semester (Reg./Pvt./ATKT) Examination, 2021
Mathematics
Paper - Compulsory
Functional Analysis-II
[Maximum Marks : Reg. 85 Pvt. 100]
Note :- All questions from each section carry equal marks. All questions are compulsory and answer limit are approximately 250 words. Start the answer of each section from new page. Maximum limit of pages of answer booklet are approximately 16 pages. Answer should be written by the student in his/her own handwriting mandatory. The first page of answersheet should be download by the student from university website is mandatory.
1.
Define orthonormal set with example. Show that an orthonormal set in linearly independent.
2.
Define self-adjoint, unitary and Normal operators and prove that, "A bounded linear operator T on a complex Hilbert space H is unitary if and only if T is isometric and surjective".
3.
Define Adjoint and Hilbert-adjoint operator. Establish relation between adjoint operator and Hilbert adjoint operator. Also give differences between the above two.
4.
Prove that every inner product space X is uniformly convex.
5.
State and prove projection theorem.