Sup norm

Related BrainMass Solutions

• Normed Space, Compactness and Transformation

  Prove that the when the interval I is compact, the set X defined above of normed spaces coincides with C(I,X), and that the sup norm and the norm ||.||_epsilon,h are equivalent.

• Prove that if A is a family of functions in C_0 such that A is uniformly bounded and equicontinuous, then every sequence of functions from A has a convergent subsequence in the sup-norm.

  A is uniformly bounded and equicontinuous, then every sequence of functions from A has a convergent subsequence in the sup-norm.

• Norm on Linear system with matrix A

  503825 Norm on Linear System with Matrix A We fix a norm II . II on R^n. If A is a real n x n matrix, define The norm II A II = sup { II Ax II : x E R^n, II x II =< 1}.

• Banach space and closed subspace

  Show that the space C(I,R^n) of continuous functions from I into R^n is a Banach space with the uniform norm llull = sup l u(t) l where t is in I. (Show that this is a norm and that C(I,R^n) is complete). See attached file.

• Linear Mapping in Subsets

  Second, I claim that is a normed spaced under sup norm. It is easy to see that for any . To show is a norm, we also need to verify the following three features. (1) For any , (2) For any , we have .

• Llinear functional on N U 0

  (c) For a bounded linear functional L: H-->F define the norm of L as follows: ||L|| = sup {|L(h)|: for all h in H such that ||h||<1 }. What is the norm of the linear functional L defined in (b)?

• Proof : Sequences and Supremum

  Thus sup{a_n+b_n}+e>=sup{a_n+b-e/2}+e=sup{a_n}+b-e/2+e=sup{a_n}+b+e/2. Therefore, sup{a_n}+b_n<sup{a_n}+b+e/2<=sup{a_n+b_n}+e.

• Real analysis

  that sup(cA)=cSupA 3-postulate a similar type of statement for sup(cA)for the case c<0.

• Thermionic emission of electrons

  1426 Thermionic emission of electrons Find the value of the thermionic current in Amp/cm<sup>2sup> for a platinum filament whose work function is 4.1 eV and temperature is 2000 K. The emission constant A is 120 A/(cm<sup>2sup> K<sup>2sup>).