Math Chapter Wise question with answer

Q01 For an orthonormal subset β of H, which of the following are equivalent? 1. β is a basis 2. β is complete 3. Span β... English · OPSC PGT 2017 Q02 Let n be a fixed natural number. Thus, the series () ≥ ∑ m m n –1 m is– English · DSSSB PGT 2021 Q03 Let {an} and {bn} be sequences of real numbers defined as a1 = 1 and for n ≥ 1, () − − − n n n+1 n n+1 n n n 2a a a... English · Haryana PGT 2018 Q04 Let (H, <..>) be an inner product space, then for a, b∈H, the relation 2 2 2 2 x y x y 2 x 2 y is known as: English · OPSC PGT 2017 Q05 According to Beach's criterion, a normed vector space X is complete if and only if every: English · OPSC PGT 2017 Q06 Let E and F are Banach spaces. T∈B(E,F) becomes an open map When it is: English · OPSC PGT 2017