# Level sets of the condition spectrum

##### Citations

2 citations

2 citations

### Cites background from "Level sets of the condition spectru..."

...The central theme of [13] is to identify and classify the Banach algebras A in which the interior of L (a) is empty for any a ∈ A and ∈ (0, 1)....

[...]

...Further, for ∈ (0, 1], the -level set of the condition spectrum of a ∈ A is defined in [13] as the following set....

[...]

1 citations

### Additional excerpts

...3 in [45], interior of L 0(A) is empty in the set {λ ∈ C : |λ| > 1}....

[...]

##### References

[...]

139,059 citations

### Additional excerpts

...If there exists a ∈ A \ Ce such that σ(a) = {λ1, λ2} with λ1 6= λ2, then by proposition 9 in §7 of [8], there exists idempotents e1 and e2 such that σ (ae1) = {λ1}, σ (ae2) = {λ2} and a = ae1 + ae2....

[...]

850 citations

### "Level sets of the condition spectru..." refers background in this paper

...It is proved in [5] that Hilbert spaces and Lp (with 1 < p < ∞) spaces are uniformly convex Banach spaces and hence they are all complex uniformly convex Banach spaces....

[...]

105 citations

### "Level sets of the condition spectru..." refers background in this paper

...One can find, some more answers related to this question in [2], [3] and [4]....

[...]

99 citations

### Additional excerpts

...A function f : Ω→ A is said to be differentiable at the point μ ∈ Ω (see [13], Definition 3....

[...]

85 citations

### "Level sets of the condition spectru..." refers background or methods in this paper

...([9], Remark) Let X be a complex Banach space....

[...]

...Step 2 : In this step we apply Theorem 2 in [9] to the functions ψn and we see the consequence....

[...]

...Applying, Theorem 2 in [9] to the function ψn, we get ‖ψn(λ)− ψn(0)‖≤ ( 2|λ| 1− |λ| ) wc (1− ‖ψn(0)‖) for all λ ∈ B(0, 1)....

[...]

...In [9], Theorem 1, Globevnik showed L1 space is complex uniformly convex....

[...]