If the dual X' of a normed linear space X is fininte dimensional, then X is finite dimensional

Q: 3. Show that in a normed space X, vector addition and multiplication by scalars are continuous…

A:

Q: Suppose V1, ..., Vn are vector spaces then does L(V1 x...x Vn, U) have the same dim with L(V1, U)…

A:

Q: Give an example with values of a nonstandard operation for M2*2 a vector space that fulfills all…

A:

Q: show that the discrete metric on u Vector space X+3 of eannot be obtained from a norm.

A: To Show: Show that the discrete metric on a vector space X ≠ 0 cannot be obtained from a norm.

Q: llnll=max |x C+)| tej show that is norme space. j-[a,b]

A: We have to show that x=maxt∈jxt, where j∈a, b, is a normed space. For this, we have to use the…

Q: If (x1,y1) + (x2,y2) = (x1x2,y1y2) and  c(x1,y1)= (cx1,cy1) are vector spaces, verify if both…

A:

Q: 2.52 Prove that Ca, b] is a vector space.

A:

Q: Prove that linear maps are bounded for multivariable calculus

A: In this question, concept of linear map is applied. Linear Map The matrix of the linear map can…

Q: Every continuous function from normed space X into normed space Y is bounded linear operator True…

A: True

Q: Define diffeomorphish between two manifolds and Completly explain why any linear map fiM_N. between…

A:

Q: 12. Show that the set of all continuous function on the interval [-1,1] is a vector space under…

A:

Q: 3. Show that X = [0; 1] with the discrete metric is bounded but not totally bounded

A:

Q: * Every Pre-Hilbert space is I - Continues Normed space -orthogonal Metric space inner Produced

A: Every pre-Hilbert Space is a complex vector space X together with an inner product (A complex inner…

Q: DATE MONTH 9- verify that l ell max alt)| defines. t elasb] %3D the Space cla,b]. morm on

A: Norm: A norm· is mapping defined on vector space V which satisfies following properties: 1. x ≥ 0,…

Q: 8.F. Ifx= (1, I, --- ,)€R", define x, by e that z- l, is a norm on R'. Prove

A: Given that x=x1,x2,..,xn and x1=x1+x2+...+xn. The objective is to find the whether x1=x1+x2+...+xn…

Q: If X is inner product space over real numbers then the inner product always greater than or equal…

A: The objective is to determine whether the given statement is true or false. Given statement is, " If…

Q: Let X be vector space of all ordered pairs. Show that ||x || = |x1| + |x2] defined norm on X %3D

A: It is required to show that: x=x1+x2 defined norm on X, where X be vector space of all ordered…

Q: Shoe that Hhe p qiuen by norm on (on ho f be given by a scalar prodluct

A: We need to show that the norm on l∞ given by: x1,x2,…,xn,…∞=supxj: j=1,2,3,… can not be given by a…

Q: If (X.r) and (X,r,) are T,-spaces, then (X.r,nt) is also a T, -space. GOOD LUCK

A:

Q: Every continuous function from normed space X into normed space Y need not be bounded linear…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: O Show that whether the functions sint and cost in the vector space C[-n, 7]of continuous functions…

A:

Q: Prove that any linear map between finite dimensional normed linear spaces is continuous.

A:

Q: ht x and y be normed spaces. Show that a Lincar operator T:Xy is bounded If and only T maps bounded…

A:

Q: Let VER, defined the addition by: %31 with standard multplication - IS V Vector sPace Just

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Prove that a linear map on a normed vector space is bounded if and only if it is continuous.

A:

Q: 0:1 Show that norm ||x|| = (Elx¡l?)ž satisfies the conditions of normed space. %3D

A:

Q: Question that R vector space is Paove under fie ld IR.

A:

Q: Show that ℝ2 is a vector space with usual addition and multiplication.

A: To prove that R2 is vector space we have to prove following; 1. R2 is abelian group under addition.…

Q: Q If X R, define the function ||- ||: R →R*u {o} by ||-|| = |x| + 1. Is (R, ||-||) normed space.…

A: Solution: We will use the following definition: The function .:ℝ→ℝ is a norm if it satisfies the…

Q: Every continuous function from normed space X into normed space Y is bounded linear operator True…

A:

Q: If them every normed lineers spare X is finite demisional Linear transformation. X is bounded a

A:

Q: Prove the locally compact normal linear space is finite dimensions.

A: We have to prove the  locally compact normal linear space is finite dimensions First we define the…

Q: 13- Suppose that W is a subspace of normed space V then it is not necessary that W is also normed…

A: Subspace of a normed space

Q: Is it true that if two vector spaces V and W both have dimension 2022, then they must be isomorphic?…

A: Suppose V and W are two vector spaces. We know that , V and W are isomorphic to each other if there…

Q: (a) If X,Y are Banach spaces on XOY _define |(x, y)|| = || +|>ly. Show that this gives a norm making…

A: If X and Y both are Banach spaces then we need to prove that X⊕Y is Banach space with respect with…

Q: If Linearly prove. Vector VCE) is spanned by dependent Set {v, V--- Vn}- "Then that V can also…

A:

Q: Give example on the inner product and same time is normed space

A: To find an example on the inner product and normed space. Definitions: Inner product space: Let V be…

Q: Every compact, Hausdorff space is normal.

A: To prove: Every compact, Hausdorff space is normal. Let X be a compact Hausdorff space. Let A,B⊂X be…

Q: The set R2 is a vector space over R. How Prove it ?

A: We need to check each and every axiom of a vector space to know that it is in fact a vector…

Q: SHOW THAT THE SET OF POLYNOMIUMS HAS A VECTOR SPACE OF POLYNOMIALS OF A LESS DEGREE THAN “g”  (Pg…

A:

Q: Prove the parallelogram law on an inner product space V; that is, showthatllx + Yll2 + llx - Yll2 =…

A: Prove the parallelogram law on an inner product space V; that is,  Show that…

Q: nduce Such that induced cosinte Sind l Meatric SPaces toplogey. write meatric Spaces Such that…

A:

Q: Consider the vector space of continuous functions over the interval [-1,1] with the inner product…

A: Given that,

Q: Verify that P,(R) = Eax | a, eR}, with addition and scalar multiplication !! 1-0 defined by Ź(a,…

A: let  k1  and k2  be two scalar  and  ∑aii=02xi   ∈P2ℝif P2ℝ is vector  space with given operation…

Q: SHOW THAT THE SET OF POLYNOMIUMS HAS A VECTOR SPACE OF POLYNOMIALS OF A LESS DEGREE THAN “g”  (Pg…

A:

Q: Let V be an inner product space with dimV = 2, and suppose that L= {u+v, u+2v} is a linearly…

A: Let V be an inner product space with dimV=2 and L=u+v,u+2v is a linearly independent subset of V.…

Q: now that Reis Banach f|xl|= | ( 2 | ², 1² ) / 2 j=1 and vector space. 2h is complete.

A: We have given Rn andx=∑j=1n  ξiq12. We have to show that Rn is Banch space, vector space and…

Q: What is Null Space?

A: We will solve the given question by giving the definition of null space. Let U and V be two vector…