For the first time since 2007, a majority of small business owners - 55 percent - are optimistic about near-term business prospects, an increase of 10 percent since March.

In addition, 26 percent reported that opportunities for their business are expanding, up from 15 percent one year prior, though this does not seem to be a direct result of the improving economy - 44 percent indicated that these opportunities are a result of less competition.

However, 63 percent of small business owners do not believe the worst of the recession is over, and almost one in six respondents said they still are at risk of going out of business within the next six months.

"There appears to be a dichotomy where many small businesses are seeing signs of improvement while other firms are still struggling to make payroll," said Susan Sobbott, president of American Express OPEN.

These findings echo another survey of small business owners released this week by Citibank, which found that 24 percent of respondents believe their share of business versus the competition has improved.