25 Questions
What type of representation is needed for the unital uff in L'(G) according to the text?
Unitary representation
What characteristic should the representation of L'(a) on H possess to ensure the unital uff in L'(G based on the text?
Non-degenerated
Which property must the representation of L'(a) on H have to result in a unital uff in L'(G according to the text?
1-1 correspondence
In the context of L'(G), what is a key requirement for the unital uff according to the text?
Being discrete
Which type of representation is crucial for ensuring the unital uff in L'(G based on the text?
Unitary
What value does 'X' represent in the text?
A variable denoting a compact space
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)
What condition must be satisfied for an element a in felp'(G) to be considered faithful?
a * a* = 0 implies a = 0
What is the result of the expression 'L M(U)² J V H(U)²'?
LM(U)²JVH(U)²
In the context of the provided text, what does 'compact' refer to?
A space that is closed and bounded
In the Gelfand-Naimark-Segal correspondence, what role does A play?
A is associated with the Gelfand-Naimark-Segal theorem
If an element a in felp'(G) satisfies sc*(a) = 0, what can be inferred?
a is a unitary operator
What operation does the symbol '[:U is compact ]]' likely represent?
Indicator function
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
What condition characterizes an element a in felp'(G) such that sc(a) = 0 implies s(a) = 0?
|a| ≥ kva
What kind of representation does A have on H according to the given text?
Irreducible
Which property does the representation S of A on H satisfy based on the provided information?
S(2) = 0
What happens to the representation S of A on H if I is ±1?
S(2) remains the same
Which term describes a representation of A on H if S(2) < 0?
Decomposable
In the context provided, what is the implication if S is not reducible?
A is decomposable
What does the function f * g * £6L² (G₂) represent in the given context?
The composition of functions f, g, and £6L² (G₂)
What is the domain of the function L'(G) in relation to function BCL²(G)?
L'(G) is a subset of BCL²(G)
Which operation does the symbol £ represent in the function notation £6L² (G₂)?
Convolution
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)
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)
Test your understanding of the 1-1 correspondence between unitary representation and non-degenerated * representation of L'(a) on H. Explore the implications if L'(G) is unital in a discrete setting.
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