Difficulty distribution
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1questions
Easy
1
100%
Functional Analysis - Mathematics Previous Year Questions
Practice Functional Analysis - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.
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1Topics
Functional Analysis question pattern
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Question type distribution
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1questions
MCQ
1
100%
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Included previous year papers
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| Paper | Year / session | Questions in this view | Open |
|---|---|---|---|
| Mathematics (MA) 2012 | 2012 | 1 | View paper |
Sample previous year questions
A varied preview from the papers represented in this selection, with every available option.
2012 · Mathematics · Functional Analysis · Normed Spaces, Banach Spaces and Operators
Mathematics (MA) 2012
Consider the statements
P: If \(X\) is a normed linear space and \(M \subseteq X\) is a subspace, then the closure \(\overline{M}\) is also a subspace of \(X\).
Q: If \(X\) is a Banach space and \(\sum x_n\) is an absolutely convergent series in \(X\), then \(\sum x_n\) is convergent.
R: Let \(M_1\) and \(M_2\) be subspaces of an inner product space such that \(M_1 \cap M_2 = \{0\}\). Then \(\forall m_1 \in M_1, m_2 \in M_2 ; \|m_1 + m_2\|^2 = \|m_1\|^2 + \|m_2\|^2\).
S: Let \(f : X \to Y\) be a linear transformation from the Banach Space \(X\) into the Banach space \(Y\). If \(f\) is continuous, then the graph of \(f\) is always compact.
The correct statements amongst the above are:
P: If \(X\) is a normed linear space and \(M \subseteq X\) is a subspace, then the closure \(\overline{M}\) is also a subspace of \(X\).
Q: If \(X\) is a Banach space and \(\sum x_n\) is an absolutely convergent series in \(X\), then \(\sum x_n\) is convergent.
R: Let \(M_1\) and \(M_2\) be subspaces of an inner product space such that \(M_1 \cap M_2 = \{0\}\). Then \(\forall m_1 \in M_1, m_2 \in M_2 ; \|m_1 + m_2\|^2 = \|m_1\|^2 + \|m_2\|^2\).
S: Let \(f : X \to Y\) be a linear transformation from the Banach Space \(X\) into the Banach space \(Y\). If \(f\) is continuous, then the graph of \(f\) is always compact.
The correct statements amongst the above are: