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Ali Taghavi
Ali Taghavi
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Let $A$ be a unital $C^*$ algebra. Assume that $D:A\to A$ is a bounded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

Motivation: I had intention to consider a simillar process to generat a kind of Legendre polynomial(a similar but not identical to it). So I wondered if requirement $D(P_1)=P_0$ is feasible for some appropriate derivation. On the other hand the impossibility $[x,y]=1$ leads us to search for outer derivation

Let $A$ be a unital $C^*$ algebra. Assume that $D:A\to A$ is a bounded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

Let $A$ be a unital $C^*$ algebra. Assume that $D:A\to A$ is a bounded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

Motivation: I had intention to consider a simillar process to generat a kind of Legendre polynomial(a similar but not identical to it). So I wondered if requirement $D(P_1)=P_0$ is feasible for some appropriate derivation. On the other hand the impossibility $[x,y]=1$ leads us to search for outer derivation

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

Let $A$ be a unital $C^*$ algebra. Assume that $D:A\to A$ is a bondedbounded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

Let $A$ be a unital $C^*$ algebra. Assume that $D:A\to A$ is a bonded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

Let $A$ be a unital $C^*$ algebra. Assume that $D:A\to A$ is a bounded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

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Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

Let $A$ be a unital $C^8$$C^*$ algebra. Assume that $D:A\to A$ is a bonded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

Let $A$ be a unital $C^8$ algebra. Assume that $D:A\to A$ is a bonded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

Let $A$ be a unital $C^*$ algebra. Assume that $D:A\to A$ is a bonded derivation.

Can one say that $1$ can not be in the image of $D$?

If the answer is no:

What is a counter example? What kind of $C^*$ algebra admits outer bounded derivation but stil they satisfy the above prevent property?

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Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123
Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123