"It did something it hasn't been able to do for a while. It's a step in the right direction. The question is can it build on that and can it get more potency. In order for it to do something, we're going to have to see some sort of news from (Apple CEO) Tim Cook and the dividend," said Scott Redler of T3Live.com.
Traders are speculating that Apple could soon announce that it would use some of its $137 billion cash pile to pay a special dividend, buy back stock or both, within a few days. They are speculating that Apple could pick a date in mid-March for an announcement, since Apple last year announced that it was initiating its first quarterly dividend and a buyback program on March 19, several weeks after its annual meeting.
"This afternoon for the first time in a long while, I actually bought some Apple," said Dennis Gartman on "Fast Money." Gartman said he hedged S&P 500 futures against Apple. "It's a bet on Apple perhaps making a bottom." Gartman is the editor of the Gartman Letter, and he turned bearish on the stock market recently, and continues to be so.
(Read More: Apple CEO Cook Talks New Music Service With Beats Electronics)
The Dow and the S&P 500 both rose for a seventh day Monday, led by the financial sector. The S&P 500 rose 5 to 1556, nine points away from its all-time closing high and about 20 points below its record intra-day high. The Dow rose 50 to 14,447, a new high, and the Nasdaq was up 8 at 3252. At the same time, the VIX, the CBOE Volatility Index, fell to 11.56, its lowest level since February, 2007.
There are two economic reports Tuesday morning -- the NFIB small business survey, at 7:30 a.m. ET and the Labor Department job openings data at 10 a.m. The Treasury auctions $32 billion in three-year notes at 1 p.m.
As for Apple, the speculation about its products is constant, but the speculation about a special dividend has really picked up since the company said it was considering ways to enhance shareholder values. The company was taken to court by hedge fund manager David Einhorn just ahead of its annual meeting last month, to stop a vote that would have made it impossible for Apple to issue a preferred without a shareholder vote. Einhorn dropped his suit after a court issued an injunction against Apple.
Oppenheimer Asset Management chief technician Carter Worth, in a note, said he believes Apple is now a buy. He says Apple's time may have come, after going on a round trip, shooting to $705 in September, then back to a low of $419 last week. During that time, the stock market moves sharply higher despite widely-held Apple's lack of participation.
(Read More: Apple Chart Looks 'So Bad Its Good')
"We are buyers here. A terrible chart, which we believe, is 'so bad that it's good,'" he wrote in a note. Worth, meanwhile, writes the sell-off in Apple is "mature in terms of magnitude (-$286...-40.6 percent) and duration (5-1/2 months in the making) leaving the stock right back at the level where the euphoric, parabolic move of 2012 got under way."
Apple has now retraced the move, Worth said, beginning on January 26 with a gap up that has since been filled.
Redler said he's now holding more Apple than he's had in a long time, and he said that traders want to be able to be long the stock. "You'd like to see a bounce. I don't think we're going to see new highs in the stock, but why not bounce back to $540/$550, where there's resistance," Redler said.
(Read More: Why Doug Kass, Marc Faber Remain Bearish on Apple)
"If it sustains this, it would be healthier for the technology sector," Redler said. "The QQQS have underperformed because of the drag of Apple." The PowerShares QQQs represent the Nasdaq 100.
As Apple and stocks crept higher Monday, a number of analysts continue to call for a correction. Janney Montgomery chief investment strategist Mark Luschini said the market could keep moving higher, for now.
"It just smacks of certainly positive risk momentum, and to some degree, complacency," he said. "Complacency has been rewarded so far."
Worth, meanwhile, said just as he likes Apple, he dislikes the stock market.
"(Apple) shares have expunged a great deal of the exuberance and hubris of the past year," Worth wrote. The 40 percent decline also has shaken out "fast money" that started chasing the stock in January of 2012.
(Read More: Complacency Could Signal Violent Selloff)
Apple is now the farthest below its 150-day moving average at any time since the stock market collapsed in the financial crisis in 2008/2009, Worth noted. That could mean the stock would move back toward the 150-day moving average, and the meet the "smoothing mechanism" around the $525 level.
"Bottom line: We are buyers of Apple here, playing for a prospective rebound...and sellers of the market here, playing for a prospective sell off," Worth notes.