Ticker symbols are too short to be protected by copyright (and the copyright would in any case belong to the exchange and not the company, since the exchange creates them). It is also not functional, so it could not have a utility patent, and is not secret, so it could not be a trade secret.
So far as I know, none of the ticket symbols are registered as trademarks under the Lanham Act (the federal trademark law in the United State). But, a company could argue that it acquired a common law trademark in its ticker symbol if it used the ticker symbol in association with the sale of goods or services.
Even if it was a trademark, however, this would not prevent it from being used in the usual way that ticker symbols are used, as a nominative use identifying a company with an abbreviation of its legal name or of a trade name, rather than in a manner that conveys the impression that one is authorized to sell goods and services under the name of the company.
In the example posed, I don't think that you could determine whether there was an infringement of common law trademark rights in a vacuum.
First, it would be necessary to determine if a particular ticker symbol had acquired a secondary meaning (i.e. an association with the company) in the relevant part of the general public. For example, "A" without some context identifying it as the ticker symbol for Agilent Technology, would obviously not be entitled to common law trademark protection.
Second, it would be necessary to examine the manner in which the ticker symbol was used.
The gravamen and gist of trademark infringement is that one misleads someone to think that you have an affiliation with a company in connection with a use of that trademark in commerce. If one is doing that, I could see a common law trademark infringement case prevailing.
For example, if one had an email that said "[email protected]" and was selling goods competing with those produced by "Americansource Bergen Corp" to people who would otherwise have brought Americansource Bergen Corp's goods, I could easily see a common law trademark infringement action prevailing with the domain name suggesting that you were a licensed affiliate of Americansource Bergen Corp who was marketing its goods, rather than the company itself.
On the other hand, if one had an email that said "[email protected]" and you were a neighbor or former employee of Americansource Bergen Corp or a family member of an employee or a customer, then there would be no basis for a common law trademark infringement action.
And, there are some cases, such as the "[email protected]" email for Equifax which on its face could almost never be construed as an attempt to mislead someone into thinking that you were authorized to sell goods or serves of Equifax.
Generally speaking, there is no such thing as a "facial" trademark infringement except perhaps when a trademark is placed directly on a good not manufactured or licensed by the trademark owner. So, there is no blanket answer to your question.