Unitary Representation and Non-Degenerated * Representation Quiz

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What type of representation is needed for the unital uff in L'(G) according to the text?

Basis representation

Non-unitary representation

Degenerated representation

Unitary representation (correct)

What characteristic should the representation of L'(a) on H possess to ensure the unital uff in L'(G based on the text?

Irreducible

Continuous

Non-degenerated (correct)

Orthogonal

Which property must the representation of L'(a) on H have to result in a unital uff in L'(G according to the text?

Non-unitary property

Discrete property

1-1 correspondence (correct)

Degenerated property

In the context of L'(G), what is a key requirement for the unital uff according to the text?

Being discrete Signup and view all the answers

Which type of representation is crucial for ensuring the unital uff in L'(G based on the text?

Unitary Signup and view all the answers

What value does 'X' represent in the text?

A variable denoting a compact space Signup and view all the answers

In the context of the text, what does it mean when a directed set U₁ and U₂ 6 4 is an approximate identity of L^(G)?

U₁ and U₂ converge to the identity in L^(G) Signup and view all the answers

What condition must be satisfied for an element a in felp'(G) to be considered faithful?

a * a* = 0 implies a = 0 Signup and view all the answers

What is the result of the expression 'L M(U)² J V H(U)²'?

LM(U)²JVH(U)² Signup and view all the answers

In the context of the provided text, what does 'compact' refer to?

A space that is closed and bounded Signup and view all the answers

In the Gelfand-Naimark-Segal correspondence, what role does A play?

A is associated with the Gelfand-Naimark-Segal theorem Signup and view all the answers

If an element a in felp'(G) satisfies sc*(a) = 0, what can be inferred?

a is a unitary operator Signup and view all the answers

What operation does the symbol '[:U is compact ]]' likely represent?

Indicator function Signup and view all the answers

Which mathematical concept is primarily involved in the expression '20 ходом.dM V.of a on se and = + H(U) [:U is compact ]] 1 Xu ; vol.'?

Volume calculation in a compact space Signup and view all the answers

What condition characterizes an element a in felp'(G) such that sc(a) = 0 implies s(a) = 0?

|a| ≥ kva Signup and view all the answers

What kind of representation does A have on H according to the given text?

Irreducible Signup and view all the answers

Which property does the representation S of A on H satisfy based on the provided information?

S(2) = 0 Signup and view all the answers

What happens to the representation S of A on H if I is ±1?

S(2) remains the same Signup and view all the answers

Which term describes a representation of A on H if S(2) < 0?

Decomposable Signup and view all the answers

In the context provided, what is the implication if S is not reducible?

A is decomposable Signup and view all the answers

What does the function f * g * £6L² (G₂) represent in the given context?

The composition of functions f, g, and £6L² (G₂) Signup and view all the answers

What is the domain of the function L'(G) in relation to function BCL²(G)?

L'(G) is a subset of BCL²(G) Signup and view all the answers

Which operation does the symbol £ represent in the function notation £6L² (G₂)?

Convolution Signup and view all the answers

What does the claim 9L²(G) imply in the context of the provided mathematical expressions?

The function 9L²(G) is equivalent to L 8 (8) Signup and view all the answers

If f and g are functions and G represents a variable, what is the interpretation of L'(G) → BCL²(G)?

A function that operates on L'(G) to produce an output in BCL²(G) Signup and view all the answers