A. B. Patel

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math.FA2023

Spatial Numerical Range in Non-unital, Normed algebras and their Unitizations

H. V. Dedania, A. B. Patel

Let $(A, ∥ \cdot ∥)$ be any normed algebra (not necessarily complete nor unital). Let $a \in A$ and let $V_{A} (a)$ denote the spatial numerical range of $a$ in $(A, ∥ \cdot ∥)$ . Let…

math.FA2023

On the convexity of spatial numetical range in normed algebras

H. V. Dedania, A. B. Patel

In this article, we address the following question: Is it true that the spatial numerical range (SNR) $V_{A} (a)$ of an element $a$ in a normed algebra $(A, ∥ \cdot ∥)$ is always conv…

math.FA2023

The Spectral extension property in the unitization of Banach Algebras

H. V. Dedania, A. B. Patel

Let $A$ be a non-unital Banach algebra and let $A_{e} = A \oplus C 1$ be the unitization of $A$ . It is true that if $A_{e}$ has the spectral extension property (SEP), then $A$ …